Vapor-phase mechanisms [e.g., vapor-liquid-solid (VLS), vapor-solid-solid, oxide-assisted growth, and the self-catalytic growth mechanisms] for the unidirectional nanowire (NW) growth are not yet well understood. For this understanding, growths of GaN and InN NWs in our laboratory, without and with the assistance of foreign element catalytic agents (FECAs), such as Au and In, were performed. GaN NW growth, in the presence of FECA identical withNi, was possible at temperatures below the Ni/Ga eutectic temperature. InN NWs were grown, in the presence of Au, and at temperatures in the vicinity of Au/In eutectic temperature. They were found to have Au at the NW tip, NW base, and NW sidewalls. Extensive investigation of the fundamentals underlying these anomalies has been carried out. The temperature dependence of the VLS mechanism has also been elucidated. A large number of available elemental and compound semiconductor NWs exhibiting similar characteristics have been considered for the investigation. Based on this investigation, a chemicophysical mechanism called the vapor-quasisolid-solid (VQS) (or vapor-semisolid-solid, or vapor-quasiliquid-solid, or vapor-semiliquid-solid) mechanism has been proposed. The cause of temperature dependence of the VLS growth under different growth conditions and growth environments, and the possible relationship between the VLS and the VQS mechanisms has been presented. To better describe the vapor-phase mechanisms, including the VQS mechanism, a unified definition of droplets has been proposed. A series of experimental evidences has been set forth to substantiate the validity of the proposed mechanism, and to justify the definition of the unified droplet model. They together appear to explain the fundamental basis of the NW growth by various mechanisms, including the VQS mechanisms. They also provide solutions of many known problems, conflicts, confusions, and controversies involving NW growth.