There was a fame time for silicon in condensed matter physics, then the graphene era came and now topological insulators are gaining lot of attention, but magnetism in condensed matter physics has remained always fascinating starting from the ancient days up to now and it will remain as one of the core topic in basic or applied physics. The improvement in the modern techniques allows one to explore magnetism in different length scales as well as in different time scales. As an effect of the improvement in experimental techniques, different magnetic anomalies are unearthed. As a result theories are getting refined and the area of magnetism progresses. From the material point of view, oxides carry the most diverse nature in condensed matter starting from high temperature superconductivity (HTS), colossal magnetoresistance, metal insulator transition etc. to ferromagnetism (FM), anti-ferromagnetism (AFM), spin glass (SG) and so on. Among this list, SG and HTS are one of the least understood topics in magnetism till today. A large research community is involved in understanding the underlying physics behind these two, especially in transition metal oxides. It has drawn attention not only due to fundamental aspects but also due to various applications in day to day life. This thesis is an attempt to understand these two phenomena in transition metal oxides. As the title of this thesis suggest, it is all about magnetic and magneto-transport properties of certain transition metal oxide (crystalline) addressing the interplay between two competing order parameters to understand the underlying physics behind it from an experimental point of view. We have studied two different kinds of competing interactions: (i) the FM/AFM interplay either in bulk or at the interface of the two layers in thin films; (ii) the interplay between FM and superconductivity (SC) in superconductor (S)/ferromagnet (F) heterostructures. Basically both of these two kinds lead to non-equilibrium phenomena in these oxides. One of such competition is between FM and AFM leading to slow dynamics (glassy physics). Disorder and frustrations are the key ingredients for such slow dynamics. The spin frustration arises either due to geometry or due to competing interactions. For example, in a triangular antiferromagnet due to the triangular geometry spins gets frustrated. Now, if it prevails spin disorder as well then it satisfies both the criteria for a spin glass and hence it gives birth to glassiness. Another kind of competition is the interplay among SC and FM. It is known that SC and FM are two antagonistic quantum phenomena thus in a single material SC (singlet pairing) and FM does not co-exist. However one can realize this by making F/S heterostructures and observe the battle between these two competing order parameters. The spin polarized quasiparticle injection from F creates non equilibrium spin density inside S and thereby suppressing the order parameter of S. Also by choosing an appropriate ferromagnet the vortex motion inside S can be arrested to certain extent which can enhance the critical current density of S. Thus FM/SC interplay has become an alternative way to look at the high temperature superconductivity. This thesis is categorized into nine chapters. The summary of each chapter is as follows: Chapter: 1 contains certain concepts of magnetism and superconductivity which is useful to understand the topics and experiments described in this thesis. Chapter: 2 gives the underlying principles of the various experimental techniques used in this thesis. Chapter: 3 describes the magnetic properties of successfully synthesized five compositions of LixNi(2-x)O2 (0.67<x<0.99) which has five distinct ground states namely antiferromagnet (AF), spin glass (SG), cluster glass (CG), re-entrant spin glass (RSG) and ferromagnet (FM). The SG and CG ground state has been well described by the frequency dependent peak shift. From the power-law divergence of critical slowing down the estimated value of relaxation time indicates the presence of interacting macro spins (spin cluster) rather than individual spins in certain LixNi(2-x)O2 samples possessing CG ground state which is also supported by the Arrhenius law. The shift in the spin freezing temperature with the application of dc field obeys Almeida-Thouless line. It also exhibits memory effect which is generic to the slow dynamics. The remnant magnetization relaxation follows logarithmic decay. Interestingly, the sample having RSG ground state shows memory effect up-to 50K and behaves like a FM above that temperature. FC-ZFC M(T) curve shows a splitting at the ordering temperature. The critical analysis across the ferromagnetic-paramagnetic phase transition yields a self-consistent γ, β and δ value and the spin-spin interaction in this material follows long range mean field model. The critical exponents obey Widom scaling law: δ = 1 + γ β −1. The universality class of the scaling relations is also verified where the scaled m and scaled h collapses into two branches. Finally the magnetic phase diagram illustrates a vivid picture of the gradual evolution of ferromagnetism in LixNi(2-x)O2 through a glassy state. As a concluding remark, we think, the present study of glassy physics in magnetic insulator/semiconductor sets an example to compare them with the conventional metallic spin glass system. Chapter: 4 exhibits the results of the structural, magnetic and transport measurements to elucidate some of the most striking unusual physical responses of bulk SrRuO3. Two set of polycrystalline SrRuO3 samples with unique ordering temperature have been synthesized. In one case, we have taken the stoichiometric weight ratio of precursors that eventually resulted in Ru-deficient SrRuO3(SROD). In the other case, we have taken extra 2% wt. RuO2 deliberately to form stoichiometric SrRuO3(SRO). Both the samples are found to crystallize in orthorhombic crystal structure with Pnma space group. The low temperature magnetization is found to be well described by the Bloch T3/2 law and the magnetization near Tc is found to follow the scaling law; M~(Tc-T)β with β=0.35 and β=0.30 for SRO and SROD respectively, apparently showing the 3D Ising behaviour. This aspect will be elaborated in the next chapter. The magnetic ac susceptibility study exhibits a broad hump far below the ferromagnetic ordering temperature and the frequency dependence of this hump position exhibits the characteristics of multiple relaxations. Most strikingly, we notice a low temperature glassy magnetic behaviour clearly demonstrated by the time dependent memory effect. This is very surprising and unlikely to happen in systems, which have itinerant ferromagnetic character. However, we conjecture that slow domain growth and spin canting could be the cause for such effect. The transport study evidences a crossover from Fermi liquid (FL) to non-Fermi liquid (NFL) behaviour around 40 K and a slope change in dρ/dT vs. T plot in the vicinity of that temperature. Astonishingly, we observe two distinct dips (one around ferromagnetic ordering temperature and the other far below the ferromagnetic ordering temperature) in the temperature dependent MR response. In addition, we also observe the signature of an unusual dip in the temperature dependent coercive field towards low temperature side. The emergence of such unusual magnetic and transport response is strongly believed to be connected with hidden magnetic interactions. Our effort on neutron diffraction study has been able to trace the cause of such cryptic magnetic interaction. The findings of neutron diffraction study evidence the change in the unit cell lattice parameters around 75 K and that could be the central cause behind such anomalous low temperature magnetic responses. It also demonstrates that the octahedral tilt freezes around the FM transition and has a minimum around the low temperature glass transition temperature. Most remarkably we observe a decline in the total integrated magnetic intensity towards the low temperature side indicating the presence of antiferromagnetic like interaction in SrRuO3. Chapter: 5 resolves the ambiguity in determining the crritical exponents in SrRuO3. Most remarkably, the application of scaling law in the FC magnetization leads a systematic change in the values of critical exponent with the measuring field in SRO. The β value changes from 0 to o.44 to to 0.29 (corresponds to mean field to Ising) with the increase in the measurement field from 10 to 2500 Oe. However, the H→0 extrapolation fields β=0.5. In order to substantiate the actual nature, the critical behavior is studied across the phase transition from the M-H isotherms. The critical analysis yields a self-consistent β, γ and δ values and the spin-spin interaction follows long range mean field δ=γ β model 1+. The critical exponents also obey Widom scaling law: δ = 1 + γ β-1 The universality class of the scaling relations is verified where the scaled m and scaled h collapses into two branches. We have also found that Ru deficiency does not affect the nature of the spin-spin interaction (though ferromagnetism gets reduced). Further the directional dependence of the critical exponent reflects the isotropic nature of the magnetic interaction. In other words the spin-spin interaction found to be: i) three dimensional, ii) long range, iii) mean field type and iv) isotropic in SrRuO3. We have also found magnetocaloric effect (calculated from the M-H isotherms) that across the phase transition. The specific heat measurements find sharp jump at the ferromagnetic transition due to the magnetic contribution of the specific heat. Chapter: 6 describes the magnetism at the SrRuO3 (SRO)/LaAlO3 (LAO) interface where SRO is an itinerant ferromagnet (FM) and LAO is non-magnetic (NM) (rather diamagnetic). Most surprisingly SRO/LAO exhibits pronounced exchange bias (EB) effect realized by observing a shift in the field cooled M-H hysteresis. Further investigation results an increasing trend of the strength of the EB with the decreases in the thickness of ferromagnetic layer. This system also displays the training effect which essentially confirms that this effect is due to EB. EB arises due to the uncompensated spins at the FM/AFM interface hence the EB effect in SRO/LAO system is unconventional. However, the origin of such AFM interaction (responsible for EB effect in FM/NM system) at SRO/LAO interface is realized and explained through the temperature dependence of the EB effect. Further, we have extensively investigated EB effect in other analogous ferromagnets, FM/FM bilayers and FM/FM superlattices. We found that La0.7Sr0.3MnO3 (LSMO) grown on LAO exhibits the signature of EB. In contrast to that La0.5Sr0.5CoO3 (LSCO) does not show any signature of EB. All the bilayers (LSMO/SRO, LSMO/LSCO and LSCO/SRO) exhibit EB and have similar kind of temperature dependence. In order to gain more insight we have grown a (LSMO/SRO)8 superlattice and observed a complex magnetic behaviour. It exhibits partial inverted magnetic hysteresis. But the system shows EB effect characterized by the shift in the FC hysteresis and training effect. All these observations essentially demonstrate that the magnetic nature of various ferromagnetisms at the interfaces can be changed by choosing a proper partner (acts like adding perturbations into one of those system which lies close to the instability region). Chapter: 7 presents the magneto-transport properties of three SRO films grown on LAO (100) of thicknesses of 12, 24 and 48 nm are studied extensively. For a one to one comparison one of the sample is also grown on STO(100). The coercivity vs. temperature in SRO(48 nm)/LAO exhibits a plateau at ~40 K. The dR/dT exhibits the low temperature hump in all the samples which very much replicates with the bulk scenario that we observed in SRO. Most strikingly the 12 nm SRO sample exhibits NFL behaviour throughout the temperature range of measurement (10-150 K). Our careful investigation reveals a cross-over from FL to NFL in all SRO thin films. The cross-over temperature increases with the increase in thickness and eventually shifts towards the bulk cross-over value. It is apt to remind that in bulk SRO we have demonstrated (by employing temperature dependent neutron diffraction) that there is a presence of antiferromagnetic like interaction at low temperature giving birth to glassiness in bulk SRO. Further, an attempt is made to understand the low temperature magneto-transport anomaly by looking into the spin fluctuation through the low frequency 1/f noise measurements. It conveys a message that there are two types of magnetic ordering present in SRO giving rise to two peaks in the temperature dependence of the relative variance. Application of magnetic field suppresses both the peaks in the relative variance. This certainly indicates that the origin of such peak is caused by the spin fluctuations and thereby it is of magnetic origin. Further we have looked into the Hall effect of a structured (Hall patterned) SRO thin film and observed regular Hall effect (RHE) as well as anomalous Hall effect (AHE) in it. Most remarkably the temperature dependence of the RHE coefficient changes its sign close to the ferromagnetic transition temperature of SRO. This implies a change of the type of the carrier as the temperature is varied. Based on these results, the carrier concentration of SRO as a function of temperature is determined. Chapter: 8 is about the magnetic and magnetotransport studies on the successfully grown high quality S/F heterostructures. The oxygen content plays a vital role in superconductivity of oxide materials thus for studying FM/SC interplay in oxides we have discussed how to achieve a high quality sample (oxygen stoichiometric). We have observed a great influence of a FM in suppressing the superconductivity in YBa2Cu3O(7-δ) (YBCO) in FM/SC heterostructures. The analysis of the out of plane M-H hysteresis reveals a significant reduction of the critical fields (HC1 and HC2) of the SC (in SRO/YBCO bilayer) which might have a great significance to understand the superconductivity in a better way (from both the perspectives: theory and experiments). Most remarkably we have found 40% enhancement of the critical current density of YBCO in SRO/YBCO bilayer. We have demonstrated that in order to see the effect of spin polarizes quasiparticle (SPQP) injection into YBCO, one should not apply more than 20mA current since Joule heating contribution wins over pair breaking effect. The SPQP injection from SRO into YBCO exhibits pair breaking effect as the TC (of the SC) shift follows I2/3 law. The resistive transitions under various applied magnetic fields and the field dependence of the activation energy confirms that the vortices are in the 2D regimes (it follows power law, U0~Hα withα=0.5) in SRO/YBCO. To get a better insight into the FM/SC interplay we have looked into two of the FM/YBCO combinations (LSCO/YBCO and LSMO/YBCO). We observe that the degree of the spin polarizations of the FMs scales with the suppression of superconductivity in YBCO which means more the spin polarization more is the suppression. We have also found out that spin polarization is not the sole parameter in suppressing superconductivity in SRO/YBCO bilayers. It also depends upon the state of magnetization of the ferromagnet. Further, we observed a significant reduction (one order) of the activation energy in LSCO/YBCO compared to SRO/YBCO which clearly indicates that the vortex dynamics might depend on other aspects as well (of the FM). It also reveals the formation of decoupled pancake vortices (pure 2D regime) in LSCO/YBCO and LSMO/YBCO bilayers whereas in case of YBCO and SRO/YBCO it is of 2D coupled type. Chapter: 9 summarizes the whole work presented in this thesis. It also discusses about few research problems which one need to look at in future.