Group III-nitride semiconductors are well suited for the fabrication of devices including visible-ultraviolet light emitting diodes, high-temperature and high-frequency devices. The wurtzite III-nitride based heterostructures grown along polar c-direction have large internal electric fields due to discontinuities in spontaneous and piezoelectric polarizations. For optoelectronic devices, such as light-emitting diodes and laser diodes, the internal electric field is deleterious as it causes a spatial separation of electron and hole wave functions in the quantum wells, which decreases emission efficiency. Growth of GaN-based heterostructures in alternative orientations, which have reduced (semipolar) or no polarization (nonpolar) in the growth direction, has been a major area of research in the last few years. The correlation between structural, optical and transport properties of semipolar and nonpolar III-nitride would be extremely useful. The thesis focuses on the growth and characterizations of semipolar and nonpolar III-nitride heterostructures by plasma-assisted molecular beam epitaxy. Chapter 1 provides a brief introduction to the III-nitride semiconductors. The importance of semipolar and nonpolar III-nitride heterostructures over conventional polar heterostructures has been discussed. Chapter 2 deals with the descriptions of molecular beam epitaxy system and working principles of different characterization tools used in the present work. Chapter 3 addresses the molecular beam epitaxial growth of nonpolar (1 1 -2 0) and semipolar (1 1 -2 2) GaN on sapphire substrates. An in-plane orientation relationship is found to be [0 0 0 1] GaN || [-1 1 0 1] sapphire and [-1 1 0 0] GaN || [1 1 -2 0] sapphire for nonpolar GaN on r-sapphire substrates. Effect of growth temperature on structural, morphological and optical properties of nonpolar GaN has been studied. The growth temperature plays a major role in controlling crystal quality, morphology and emission properties of nonpolar a-plane GaN. The a-plane GaN shows crystalline anisotropy nature and it has reduced with increase in the growth temperature. The surface roughness was found to decrease with increase in growth temperature and film grown at 760°C shows reasonably smooth surface with roughness 3.05 nm. Room temperature photoluminescence spectra show near band emission peak at 3.434 -3.442 eV. The film grown at 800 ºC shows broad yellow luminescence peak at 2.2 eV. Low temperature photoluminescence spectra show near band emission at 3.483 eV along with defect related emissions. Raman spectra exhibit blue shift due to compressive strain in the film. An in-plane orientation relationship is found to be [1 -1 00] GaN || [1 2-1 0] sapphire and [-1 -1 2 3] GaN || [0 0 0 1] sapphire for semipolar GaN on m-plane sapphire substrates. The surface morphology of semipolar GaN film is found to be reasonably smooth with pits on the surface. Room temperature photoluminescence shows the near band emission (NBE) at 3.432 eV, which is slightly blue shifted compared to the bulk GaN. The Raman E2 (high) peak position observed at 569.1 cm1. Chapter 4 deals with the fabrication and characterizations of Au/nonpolar and Au/semipolar GaN schottky diodes. The temperature-dependent current–voltage measurements have been used to determine the current mechanisms in Schottky diodes fabricated on nonpolar a-plane GaN and semipolar GaN epilayers. The barrier height (φb) and ideally factor (η) estimated from the thermionic emission model are found to be temperature dependent in nature indicate the deviations from the thermionic emission (TE) transport mechanism. Low temperature I-V characteristics of Au/ GaN Schottky diode show temperature independent tunnelling parameter. Barrier heights calculated from XPS are found to be 0.96 eV and 1.13 eV for Au/nonpolar GaN and Au/semipolar GaN respectively. Chapter 5 demonstrates the growth of InN on r-sapphire substrates with and without GaN buffer layer. InN film and nanostructures are grown on r-sapphire without GaN buffer layer and they are highly oriented along (0002) direction. The electron microscopy study confirms the nanostructures are vertically aligned and highly oriented along the (0001) direction. The Raman studies of InN nanostructures show the SO modes along with the other possible Raman modes. The band gap of InN nanostructures is found to be 0.82 eV. InN grown with a-plane GaN buffer shows nonpolar orientated growth. Growth temperature dependent studies of nonpolar a-plane InN epilayers are carried out. The valence band offset value is calculated to be 1.31 eV for nonpolar a-plane InN/GaN heterojunctions. The heterojunctions form in the type-I straddling configuration with a conduction band offsets of 1.41 eV. Chapter 6 deals with the temperature dependent I-V characteristics of the nonpolar a-plane (1 1 -2 0) InN/GaN heterostructures. The measured values of barrier height and ideality factor from the TE model show the temperature dependent variation. The double Gaussian distribution has mean barrier height values ( ϕb ) of 1.17 and 0.69 eV with standard deviation (σs ) of 0.17 and 0.098 V, respectively. The modified Richardson plot ln (Is/T2)-q2σ2/2k2T2 ) versus q/kT in the temperature range of 350 – 500 K, yielded the Richardson constant of 19.5 A/cm2 K2 which is very close to the theoretical value of 24 A/cm2 K2 for n-type GaN. The tunneling parameters E0 found to be temperature independent at low temperature range (150 –300 K). Chapter 7 concludes with the summary of present investigations and the scope for future work.