Gallium nitride is one of the most promising materials for ultraviolet and blue light-emitting diodes and lasers. Both Molecular Beam Epitaxy (MBE) and Metal-Organic Chemical Vapor Deposition (MOCVD) have recently made strong progress in fabricating high-quality epitaxial GaN thin films. In this paper, we review materials-related issues involved in MBE growth. We show that a strong understanding of the unique meta-stable growth process allows us to correctly predict the optimum conditions for epitaxial GaN growth. The resulting structural, electronic and optical properties of the GaN films are described in detail.