Group III-nitride semiconductors have received much research attention and witnessed a significant development due to their ample applications in solid-state lighting and high-power/high-frequency electronics. Numerous growth methods were explored to achieve device quality epitaxial III-nitride semiconductors. Among the growth methods for III-nitride semiconductors, molecular beam epitaxy provides advantages such as formation of abrupt interfaces and in-situ monitoring of growth. The present research work focuses on the growth and characterizations of III-nitride based epitaxial films, nanostructures and heterostructures on c-sapphire substrate using plasma-assisted molecular beam epitaxy system. The correlation between structural, optical and electrical properties of III-nitride semiconductors would be extremely useful. The interfaces of the metal/semiconductor and semiconductor heterostructures are very important in the performance of semiconductor devices. In this regard, the electrical transport studies of metal/semiconductor and semiconductor heterostructures have been carried out. Besides, studies involved with the defect induced room temperature ferromagnetism of GaN films and InN nano-structures have also been carried out. The thesis is organized in eight different chapters and a brief overview of each chapter is given below. Chapter 1 provides a brief introduction on physical properties of group III-nitride semiconductors. It also describes the importance of III-nitride heterostructures in the operation of optoelectronic devices. In addition, it also includes the current strategy of the emergence of room temperature ferromagnetism in III-nitride semiconductors. Chapter 2 deals with the basic working principles of molecular beam epitaxy system and different characterization tools employed in the present work. Chapter 3 describes the growth of GaN films on c-sapphire by plasma-assisted molecular beam epitaxy. The effects of N/Ga flux ratio on structural, morphological and optical properties have been studied. The flux ratio plays a major role in controlling crystal quality, morphology and emission properties of GaN films. The dislocation density is found to increase with increase in N/Ga flux ratio. The surface morphologies of the films as seen by scanning electron microscopy show pits on the surface and found that the pit density on the surface increases with flux ratio. The room temperature photoluminescence study reveals the shift in band-edge emission towards the lower energy with increase in N/Ga flux ratio. This is believed to arise from the reduction in compressive stress in the GaN films as it is evidenced by room temperature Raman study. The transport studies on the Pt/GaN Schottky diodes showed a significant increase in leakage current with an increase in N/Ga ratio and is found to be caused by the increase in dislocation density in the GaN films. Chapter 4 deals with the fabrication and characterization of Au/GaN Schottky diodes. The temperature dependent current–voltage measurements have been used to determine the current transport mechanism in Schottky diodes. The barrier height (φb) and the ideality factor (η) are estimated from the thermionic emission model and are found to be temperature dependent in nature, indicating the existence of barrier height inhomogeneities at the Au/GaN interface. The conventional Richardson plot of ln(Is/T2) versus 1/kT gives Richardson constant value of 3.23×10-5 Acm-2 K-2, which is much lower than the known value of 26.4 Acm-2 K-2 for GaN. Such discrepancy of Richardson constant value was attributed to the existence of barrier height inhomogeneities at the Au/GaN interface. The modified Richardson plot of ln(Is/T2)-q2σs2/2k2T2 versus q/kT, by assuming a Gaussian distribution of barrier heights at the Au/GaN interface, provides the Schottky barrier height of 1.47 eV and Richardson constant value of 38.8 Acm-2 K-2 which is very close to the theatrical value of Richardson constant. The temperature dependence of barrier height is interpreted on the basis of existence of the Gaussian distribution of the barrier heights due to the barrier height inhomogeneities at the Au/GaN interface. Chapter 5 addresses on the influence of GaN underlayer thickness on structural, electrical and optical properties of InN thin films grown using plasma-assisted molecular beam epitaxy. The high resolution X-ray diffraction study reveals superior crystalline quality for the InN film grown on thicker GaN film. The electronic and optical properties seem to be greatly influenced by the structural quality of the films, as can be evidenced from Hall measurement and optical absorption spectroscopy. Also, we present the studies involving the dependence of structural, electrical and optical properties of InN films, grown on thicker GaN films, on growth temperature. The optical absorption edge of InN film is found to be strongly dependent on carrier concentration. Kane’s k.p model is used to describe the dependence of optical absorption edge on carrier concentration by considering the non-parabolic dispersion relation for carrier in the conduction band. Chapter 6 deals with the analysis of the temperature dependent current transport mechanisms in InN/GaN heterostructure based Schottky junctions. The barrier height (φb) and the ideality factor (η) of the InN/GaN Schottky junctions are found to be temperature dependent. The temperature dependence of the barrier height indicates that the Schottky barrier height is inhomogeneous in nature at the heterostructure interface. The higher value of the ideality factor and its temperature dependence suggest that the current transport is primarily dominated by thermionic field emission (TFE) other than thermionic emission (TE). The room temperature barrier height and the ideality factor obtained by TFE model are 1.43 eV and 1.21, respectively. Chapter 7 focuses on the defect induced room temperature ferromagnetism in Ga deficient GaN epitaxial films and InN nano-structures grown on c-sapphire substrate by using plasma-assisted molecular beam epitaxy. The observed yellow emission peak in room temperature photoluminescence spectra and the peak positioning at 300 cm-1 in Raman spectra confirms the existence of Ga vacancies in GaN films. The ferromagnetism in Ga deficient GaN films is believed to originate from the polarization of the unpaired 2p electrons of nitrogen surrounding the Ga vacancy. The InN nano-structures of different size are grown on sapphire substrate, the structural and magnetic properties are studied. The room temperature magnetization measurement of InN nano-structures exhibits the ferromagnetic behavior. The saturation magnetization is found to be strongly dependent on the size of the nano-structures. Finally, Chapter 8 gives the summary of the present work and the scope for future work in this area of research.