Epitaxial growth of thin films of material for a wide range of applications in electronics, optoelectronics, and magneto-optics is a critical activity in many industries. The original technique, in most instances, was liquid-phase epitaxy (LPE) as this was the simplest and often the cheapest route to producing device-quality layers. While some production processes are still based on LPE, most of the research activities and, increasingly, much of the production of electronic and optoelectronic devices is now centered on metal organic chemical vapor deposition (MOCVD) and molecular beam epitaxy (MBE). These latter techniques are more versatile, although the equipment is more expensive, and can readily produce multilayer structures with atomic-layer control, which is becoming more and more fundamental to the nanoscale engineering being called upon now to produce device structures in as-grown multilayers. This chapter covers these three basic techniques, including some of their more common variants, and outlines the relative advantages and disadvantages of each of them. Some examples of growth in various materials systems of importance are also outlined for each of the three techniques.