Recent developments in the structural analysis of GaN and AlN surfaces are reviewed, and the implications of these structures for molecular beam epitaxial growth are discussed. The GaN(0001), AlN(0001), and GaN ) 0 1 10 ( surfaces are all found to be terminated by metallic layers containing approximately one bilayer of Ga or Al atoms. However, in contrast to GaN(0001) where the Ga-bilayer exists in an incommensurate, fluid-like state at room temperature, the metallic layers for AlN(0001) and GaN ) 0 1 10 ( form large-unit-cell commensurate structures with static atomic arrangements. Small amounts of H on the GaN(0001) surface leads to facet formation on the surface, whereas larger amounts of H produce a new 2×2 surface arrangement that displaces the Gabilayer. A possible model for the H-terminated GaN ) 1 1 10 ( surface is introduced and first-principles total energy calculations employing a finite temperature thermodynamics approach are employed to determine the conditions in which it could be stable.