GaN and its alloys have emerged as the leading wide bandgap materials system for electronics and optoelectronics applications despite the high extended defect densities encountered in state-of-the-art device material. Pure edge character ('a' Burgers vector) or mixed character ('a+c' Burgers vector) threading dislocations with densities in the mid-108 to 1010 level are the predominant extended defects in high quality MOCVD-grown GaN on sapphire or silicon carbide substrates. We review the origin of these along with other extended defects (e.g., stacking disorder and inversion domains) and relate the growth to basic capillary-governed growth phenomena. Recently, a new technique, lateral epitaxial overgrowth (LEO), has emerged as a technique to reduce the density of extended defects by 3 - 4 orders of magnitude. The basic growth processes and extended defect evolution in LEO growth will be presented LEO GaN can also be used to directly compare the physical properties of dislocation-free and dislocated GaN. We show in experiments on LEO and 'normal' (bulk) GaN that threading dislocations behave as charged scattering centers, non-radiative recombination centers, and current leakage paths. Additionally, threading dislocations are the most common origin of deviations from planar growth and lead to a variety of kinetically-limited growth morphologies. Finally, highlights of some of our recent work on MBE growth of GaN will be presented, including record mobilities for 2-dimensional electron gas in AlGaN/GaN heterostructures.