A review of MeV-ion beam induced crystallization (IBIEC) and interfacial amorphization (IBIIA) in III-V compounds (GaAs, InAs, GaP, InP) is given. The kinetics of IBIEC and IBIIA is studied as a function of the temperature, the density of the displacements v, and the ion dose rate j. Reversal temperatures TR for IBIEC ↔ IBIIA transitions are determined for the different materials showing characteristic dependences on v and j. The IBIEC rate is shown to be controlled by point defect diffusion towards the a/c-interface and additionally modified by the interface structure. The suppression of microtwin and stacking fault formation during IBIEC is explained by the fact that the ion beam modifies the orientation dependence of the crystallization kinetics avoiding the disintegration and (111)-faceting of the (100)-interface. For all the compound materials investigated the IBIEC process is stopped above critical temperatures and doses. The capture of diffasing defects by crystallites growing in the amorphous layers is considered to be responsible for the stopping of the IBIEC interface. Ways are demonstrated to avoid stopping, to achieve complete epitaxial regrowth also of thick layers, and to minimize the generation of stable damage in the crystallized layers. The limited temperature ranges for undisturbed IBIEC and IBIIA in III/V-compounds are explained by low nucleation barriers and high growth rates both of crystallites and of amorphous zones.