Crystal Phases in III--V Nanowires: From Random Toward Engineered Polytypism

III-V nanowires (NWs) are promising for a wide range of applications, ranging from optics to electronics, energy, and biological sensing. The structural quality of NWs is of paramount importance for the performance of such future NW-based devices. Random structural defects and polytypism occur naturally in semiconductor NWs, but progress both on the theoretical understanding and experimental control have been achieved recently. Here, we review progress towards the realization of perfect wurtzite and zinc-blende phases in III-V NWs, eventually leading to true phase engineering in single NWs.