Recently several hexagonal polytypes such as 2H, 4H, and 6H have been discovered for conventional III-V semiconductor compounds in addition to the cubic 3C zinc-blende polytype by investigating nanorods grown in the [111] direction in different temperature regimes. Also III-mononitrides crystallizing in the hexagonal 2H wurtzite structure under ambient conditions can be deposited in zinc-blende geometry using various growth techniques. The polytypic crystal structures influence the local electronic properties and the internal electric fields due to the spontaneous polarization in non-cubic crystals.In this paper we give a comprehensive review on the thermodynamic, structural, and electronic properties of twelve Al, Ga, and In antimonides, arsenides, phosphides, and nitrides as derived from ab initio calculations. Their lattice parameters, energetic stability, and characteristic band structure energies are carefully discussed and related to the atomic geometries of the polytypes. Chemical trends are investigated. Band offsets between polytypes and their consequences for heterocrystalline structures are derived. The described properties are discussed in the light of available experimental data and previous computations. Despite several contradictory results in the literature, a unified picture of the III-V polytypes and their heterocrystalline structures is developed.