Physical systems having dimensions smaller than, or of the same order of magnitude as, the characteristic length scale relevant to a physical property are referred to as mesoscopic physical systems. Due to the dimensions of the system, several physical properties get affected and this could reveal interesting physics which would other-wise have not been apparent. In the recent times, a lot interesting applications have resulted from such studies. The fundamental length scale in ferromagnetic systems is the exchange length. It is related to the magnetic anisotropy and exchange constants. Other length scales such as the size of a magnetic domain or a domain wall depends on the minimisation of energy associated with this length scale along with other factors such as zeeman energy, magnetostatic, magnetoelastic and anisotropy energies. Ultrathin magnetic films have thickness smaller than the exchange length. In this thickness regime, the surface of the film plays an important role. The magnetic anisotropy energy would get a significant contribution from the surface of the film and if it dominates over the volume contribution, would eventually lead to magnetisation pointing out of the plane of the film as opposed to imposition of demagnetising fields. Examples for such cases are FePt(L10 phase) films and Co(0001) films. Such films are important in memory applications where perpendicularly magnetised recording media are desired. When the lateral dimensions of thin films are reduced, demagnetising fields become even more important. Depending on the anisotropy in the system, certain domain patterns get stabilised in the final structure. This has led to important applications in the field of magnonics. The use of angular momentum transfer from spin polarised electrons to change the configuration of magnetisation of structured magnetic films has led to interesting memory and oscillator applications. The underlying physical parameter that needs to be controlled and carefully studied in all these cases is the magnetic anisotropy. It is favourable to have uniaxial magnetic anisotropy for memory and oscillators. This thesis chiefly deals with Fe/GaAs(001) systems. The choice of the physical system follows interest in spintronics where spin injection is desired into a semiconductor from a ferromagnet. The thesis is organized into chapters as follows. Chapter 1 attempts to introduce the reader to some of the basic concepts of mag-netism and some magnetic phenomena. The characteristic nature of a ferro-magnetic material is its spontaneous magnetisation due to long range ordering below the Curie temperature. But the moment is coupled, through some in-teractions, to spatial co-ordinates which leads to spatial variation of magnetic properties. Such interactions are also responsible for the formation of magnetic domains. The spatial variation of magnetic properties within a ferromagnet is called magnetic anisotropy. A major part of the thesis deals with the study of magnetic anisotropy of Fe thin films grown on GaAs(001) substrates. For a better understanding, the structure of the semiconductor is introduced first before discussing the influence of the structure of GaAs on the growth of Fe. A short description of the uniaxial magnetic anisotropy in Fe films is given before starting on an exploration of some possible reasons for it. Concepts of ferromagnetic resonance, spin torque effect and micromagnetic simulations are given. Chapter 2 gives a brief description of some of the experimental apparatus that was setup during the course of the research along with an overview of the differ-ent sample preparation and characterisation techniques used. The chapter is organised according to the general functionality of the techniques. Some con-cepts such as the use of low energy electrons, nanostructuring etc are introduced along with the corresponding techniques since it is best understood along with the instrumentation. Chapter 3 reports some surprising findings about the in-plane magnetic anisotropy in Fe films grown on an MgO underlayer. Until now, it has been understood that such films should exhibit only a four-fold magnetic anisotropy within the plane of the film. But the Fe/MgO/GaAs(001) films studied here exhibited an in-plane uniaxial magnetic anisotropy(IPUMA). IPUMA is dominant upto about 25 ML of Fe in case of Fe/MgO/GaAs(001) films whereas, in Fe/GaAs(001) films it is dominant only upto about 15 ML. Thus, the presence of the MgO film even appeared to enhance the uniaxial anisotropy as compared to the Fe/GaAs(001) films. In the ferromagnetic resonance (FMR) spectra, as many as three peaks were observed in Fe/GaAs(001) films of thickness 50 ML close to the hard axis of magnetisation. This means that three could be three energy minima possibly due to a competition between the anisotropies involved. Chapter 4 elaborates the investigations of the effect of orientation and doping con-centration of the GaAs substrate on the magnetic anisotropy of Fe/GaAs(001) films. It is found that doping the substrate (n type) reduces the strength of the IPUMA in Fe/GaAs films. In the wake of the long-standing debate of electronic structure v/s stress as the origin of the IPUMA in Ferromagnet/Semiconductor films, this result is important because it implies that the electronic structure of the Fe/GaAs interface influences the magnetic anisotropy. But stress, as a cause of IPUMA cannot be ruled out. The influence of deposition techniques on magnetic anisotropy is also investigated. Chapter 5 presents a way of manipulating magnetic anisotropy, and hence mag-netisation dynamics, by nanostructuring of epitaxial Fe films. It is based on the property that magnetic anisotropy of Fe films is thickness dependent. It is demonstrated that using techniques of nanostructuring, a 2 dimensional mag-netic system with controllable variation of local magnetic anisotropy is created. Such a system could be a potential magnonic crystal. chapter 6 demonstrates the proof of concept of a new memory device where memory is stored in the magnetic domain configuration of a ring in relation to that of a nano-wire. Switching between the memory states is acheived through spin trasfer torque of an electric current passing through the device, whereas read-out of the memory state is through the measurement of resistance of the device. Devices are made using NiFe and Co; it is seen that the behaviour of the devices can be explained taking into account the anisotropic magnetoresistance of the material used. Finally, the various results are summarised and a broad outlook is given. Some possible future research related to the topics dealt within this thesis is discussed.