The nature of interactions of fundamental particles is governed by symmetries. These interactions are well described by an elegant and simple SU(3)c x SU(2)L x U(1)Y symmetric gauge theory that we call the Standard Model (SM) of particle physics. Very recently the CMS and ATLAS experiments at the Large Hadron Collider (LHC) confirmed the discovery of a boson of mass of about 125 GeV. Already, the data collected from these experiments seem to indicate that this particle is in fact the last missing piece and essential ingredient of the Standard Model : the Higgs boson. The Higgs has the very distinct role of providing a mechanism through which masses for other particles can be generated without destroying gauge invariance and hence the renormalizability of the theory. While this discovery completes the picture we have of the SM, the SM itself does not account for several experimentally observed phenomena , notably, dark matter (DM) and the baryon asymmetry in the universe (BAU). From a theoretical perspective a possibility for gauge coupling unification, an explanation for the quark flavour structure and the stability of the Higgs mass to radiative corrections are features that are absent in the framework of SM. This provides a strong basis to the hypothesis that there must be some intermediate scale (between the Planck scale and electroweak scale) of new physics, i.e. physics beyond the SM (BSM). The renormalizability of SM guarantees that various parameters of SM can be determined from the electroweak scale all the way up to the Planck scale. It is interesting to note that the RG evolution of the Higgs quartic coupling is driven to smaller values and can also become negative as the energy scale increases. Naively, a negative quartic coupling indicates destabilization of the EWSB vacuum. The energy scale at which the quartic coupling becomes negative would signify a break down of the theory and would set a scale for new physics. In principle the potential can be made stable through Planck scale dynamics and other vacua (other than the EWSB vacuum) may crop up. In this scenario the EWSB vacuum may decay to the deeper vacua. It is safe to say that, within experimental uncertainties of the Higgs and top quark masses the EWSB vacuum appears to be metastable. We are now left clueless: neither do we have any hints as to the nature of BSM physics nor the scale at which SM breaks down and new physics is assured. One should also note that although the evidence for BSM is compelling, data analysed from 7 and 8 TeV runs of the LHC have not produced any signals of BSM physics so far. Thus any indications of TeV scale BSM physics have been eluding us. In such a scenario the Higgs boson has assumed the role of a portal to study the possibilities of new physics. This is also motivated by the key role that the Higgs plays in generation of mass in a gauge symmetric theory. It is therefore reasonable to assume that the Higgs boson does in fact couple to particles predicted in BSM physics. Such couplings would play a role in modifying the properties of this boson. It is now essential to determine the properties of the Higgs as precisely as possible to search for signs of BSM. This thesis explores the idea of using the Higgs as a portal to study BSM physics. The properties of the Higgs that have already been measured with data from the first two runs of the LHC are its mass, branching ratios, spin and CP. When placed in the framework of a particular new physics model, these properties impose restrictions on the couplings and masses of BSM particles. A strong candidate for a BSM scenario is a Supersymmetric extension of the SM. Supersymmetry is an extension of the Poincar´e group that describes space time symmetries. Fermionic and bosonic degrees of freedom are mixed through the generators of this extended symmetry. In the minimal supersymmetric extension of the SM (MSSM), each particle of SM has a corresponding superpartner with identical quantum numbers modulo its spin. Since we do not see, for example, a bosonic superpartner of the fermionic top quark of the same mass as that of the top quark, this must mean that the supersymmetry, even if it is realized in nature, is not exact and must be broken. Although the symmetry may be broken the MSSM has some very appealing features: stabilization of the Higgs mass to quantum corrections, gauge coupling unification and possible dark matter candidate if the lightest Supersymmetric particle happens to be both stable and neutral. It is interesting to note that in MSSM, the tree level Higgs mass is bounded from above by the Z boson mass ( ~90 GeV ). The measured value of the Higgs mass (~126 GeV ) is still achievable in the MSSM through quantum corrections, the largest contribution coming from the top quarks and stop squarks. One therefore sees that the mass of the Higgs can already provide information about top superpartners. The presence of additional charged and coloured scalars implies the possibility of existence of charge and colour breaking (CCB) minima which would affect the stability of the Electroweak Symmetry breaking (EWSB) minima generated by the Higgs potential. Stability of EWSB is then dependent on parameters in the scalar sector of MSSM. We explore the nexus between the Higgs mass and vacuum stability in this model and find restrictions on the MSSM parameter space. The lighter Higgs of the MSSM couples differently to SM particles than the SM Higgs boson. More specifically one expects the couplings of the MSSM Higgs to gauge bosons to be smaller than in SM and unlike the SM Higgs, up type quarks have couplings strengths that are different from that of down type quarks. In the decoupling regime these differences become negligible and the lighter MSSM Higgs behaves identically to the SM Higgs. The measured Higgs rates do not show any large deviations from the expectations of a SM Higgs. It is therefore reasonable to assume that MSSM, if realized, resides in the decoupling regime. While tree level processes are not altered significantly in this regime, the same cannot be said about loop induced processes such as (h→ γγ) or (gg → h). Such processes may be affected significantly by sparticles running in the loops. Higgs decays to two photons can be strongly affected by the stau sector of MSSM and we study this in connection with EWSB vacuum stability. In several models of dark matter, the dark matter candidate particle couples to the Higgs boson. It may well be that this candidate particle may be light enough so that the decay of the Higgs boson to these particles may be possible. For example, in the framework of the MSSM, the LSP (˜χ01) is the dark matter candidate and a decay of the form hχ˜→01χ˜01is possible depending on the mass and strength of coupling of such a particle. At the LHC this would show up as an branching ratio to particles that are invisible to the detectors. The dominant production mode of the Higgs at LHC proceeds through gluon fusion. In this channel a signal for an “invisibly” decaying Higgs would show up as missing energy plus jets at LHC. This has already been studied in quite some detail. We focus on other production modes, namely Vector Boson Fusion (VBF) and associated production (VH), in determining an invisible branching fraction at LHC. These two production channels are much less sensitive to any other BSM signals that may mimic an invisibly decaying Higgs and thus provide clean signals for the latter. A determination of the nature of interactions between the Higgs and gauge bosons is of paramount importance. An understanding of these interactions is closely tied to an understanding of the nature of EWSB. There are two aspects to probing these interactions. One is a determination of the Lorentz structure of the Higgs and gauge boson vertices and the second is to determine the strength of its couplings. The Higgs coupling to two gauge bosons (the hVV vertex) in SM is of the form ~ agµν . Under the assumption that BSM physics does not alter this Lorentz structure, information about possible new physics can be simply extracted through a determination of the strength of the coupling aV . However, the most general structure of this vertex is of the form (aV gµν + bV pµq ν + cV ɛ µνρσpρqσ) . Here p and q are the sum and difference of the two gauge boson momenta respectively and ɛµνρσ the completely antisymmetric Levi-Civita tensor. The term cV parametrizes CP-odd couplings while the rest are CP-even. The terms proportional to b V and cV may be generated by new physics. But which new physics model do we look at? There are a plethora of such models. Rather than shooting in the dark at random BSM directions one could adopt the following approach. In the absence of BSM signals at the LHC so far, one could assume that the scale of physics is relatively high and BSM particles are more massive than SM particles and can therefore be integrated out of the Lagrangian. It is also prudent to assume that new physics respects the SU(3)c x SU(2)L x U(1)Y gauge symmetry of SM. With these two assumptions in hand, one could supplement the SM Lagrangian with additional operators. These operators which generally have mass dimensions greater than four would destroy the renormalizability of the theory, though an interpretation as an effective theory up to a scale Λ is still valid. The idea is to now study the consequences that this effective theory would have on measurable properties of the Higgs. The effective theory could affect both the Lorentz structure as well as the strength of the couplings of the Higgs to the gauge bosons. This thesis deals with the determination of the Lorentz structure of the Higgs coupling to two gauge bosons , i.e the trilinear vertex. An analysis of this for the hZZ vertex has already been performed by ATLAS and CMS using h → ZZ *decays. A pure pseudoscalar Higgs (cZ ≠0, aZ = bZ = 0) coupling has been ruled out at about 2 ~ 3 σ level. Bounds have also been placed on a mixed scalar-pseudoscalar coupling (a Z =0,cZ =0,bZ = 0). This however, is not the end of the story. There are two important points to note here. Firstly it is important to be able to verify these findings in other production modes. To this end, we investigate the ability of VBF production to probe such anomalous couplings and find strong effects on the pseudo-rapidity distributions of the tagging jets in VBF. Secondly it is important to also look for such anomalous couplings in the hWW vertex. At this point, one might argue that the hZZ vertex and hWW vertex are connected by Custodial symmetry. However this symmetry is violated in SM by gauging of the hypercharge. It follows that violations of this symmetry should arise naturally in BSM physics. A study of the anomalous vertex is not easily achieved in h→ WW ∗ decays due to backgrounds and difficulties in reconstructing momenta. The VBF channel can be quite effective here although there is significant contamination from VBF production through the Z boson. We find that a cleaner production mode to use would be associated production. Until recently the low cross-section of Vh made it difficult to analyse this channel at LHC. An analysis of Vh has been made possible by the use of modern jet substructure techniques using (h→ bb) decays. We use these techniques and study how one can probe anomalous couplings in the Vh production mode at LHC. One of the most important couplings of the Higgs is that to the top, the heaviest SM particle. Not only is this coupling responsible for the main production channel of the SM Higgs at the LHC but the interaction with the top also has important consequences on spontaneous symmetry breaking within the SM – notably, vacuum stability arguments – as well as beyond the SM – supersymmetry, for instance, where the top drives electroweak symmetry breaking in some scenarios. The strength as well as the CP property of the Higgs top coupling is therefore an important aspect of to study. more specifically we investigate terms of the form ψ¯t(at + ibtγ5)ψth. here ψt and h corresponds to the top quark and Higgs fields respectively. at and bt parametrize scalar and pseudoscalar couplings respectively. Since the dominant production mode of the Higgs at the LHC (gluon fusion) proceeds through a top quark loop as do decays of the Higgs to two photons, some information about these couplings may be extracted just by looking at Higgs production and decay rates. However, an unambiguous determination of these couplings is possible only through Higgs production with a top and anti-top pair. Although the production rates are very small at the LHC, such a study is of prime importance. We investigate t¯th production at the LHC and list some useful observable that can probe the couplings described above. The outline of the thesis is as follows. We start with brief introduction to SM and Electroweak Symmetry breaking (EWSB) also briefly reviewing SM Higgs production and decay at the LHC. We then investigate the information that the Higgs mass in conjunction with stability of the EWSB vacuum provides about the stop sector of the MSSM. We further investigate the information that Higgs decay rates in conjunction with the stability of the EWSB vacuum could provide about the stau sector in the MSSM. We move on to examining the extent to which an invisible branching ratio of the Higgs could be measured or excluded directly at the LHC. Coming to the second part of the thesis we examine in a model independent way the nature of the Higgs-gauge boson couplings. We first give a brief description of the Higgs gauge boson vertex and the effective theory approach following it up with a description of how this could be probed using Higgs decays. We then follow it up with a study on how the Lorentz structure could affect Higgs production in Vector Boson fusion and Higgs production in association with W or Z boson. Finally, we show how the CP properties of the Higgs coupling to the top quark can be investigated using tth production along with Higgs rates.