Some of the most significant and challenging goals in the advancement of surface-emitting semiconductor lasers include realizing high-brightness sources. A promising method for increasing the optical power is to combine or optical couple the light output of multiple lasers into a single coherent beam. There have been a variety of methods used to achieve optical coupling in two-dimensional vertical-cavity surface-emitting lasers (VCSELs), which include injection locking, evanescent coupling, diffractive coupling, and anti-guiding or leaky-mode laser coupling. This chapter will focus on the physical principles of these different coupling mechanisms and how they are incorporated into two-dimensional VCSEL arrays. First, a review of beam-combining methods and the metrics used to quantify their performance is presented. The advantages of coherent beam combining over incoherent beam combining is shown as well as the necessity of optical coupling for establishing coherence across a laser array. The general discussion of the optical-coupling physics for each method will be supplemented by specific examples of two-dimensional VCSEL array coupling.