Ion-beam-induced amorphization in Si has attracted significant interest since the beginning of the use of ion implantation for the fabrication of Si devices. A number of theoretical calculations and experiments were designed to provide a better understanding of the mechanisms behind the crystal-to-amorphous transition in Si. Nowadays, a renewed interest in the modeling of amorphization mechanisms at atomic level has arisen due to the use of preamorphizing implants and high dopant implantation doses for the fabrication of nanometric-scale Si devices. In this paper we will describe the most significant experimental observations related to the ion-beam-induced amorphization in Si and the models that have been developed to describe the process. Amorphous Si formation by ion implantation is the result of a critical balance between the damage generation and its annihilation. Implantation cascades generate different damage configurations going from isolated point defects and point defect clusters in essentially crystalline Si to amorphous pockets and continuous amorphous layers. The superlinear trend in the damage accumulation with dose and the existence of an ion mass depending critical temperature above which it is not possible to amorphize are some of the intriguing features of the ion-beam-induced amorphization in Si. Phenomenological models were developed in an attempt to explain the experimental observations, as well as other more recent atomistic models based on particular defects. Under traditional models, amorphization is envisaged to occur through the overlap of isolated damaged regions created by individual ions (heterogeneous amorphization) or via the buildup of simple defects (homogeneous amorphization). The development of atomistic amorphization models requires the identification of the lattice defects involved in the amorphization process and the characterization of their annealing behavior. Recently, the amorphization model based on the accumulation and interaction of bond defects or IV pairs has been shown to quantitatively reproduce the experimental observations. Current understanding of amorphous Si formation and its recrystallization, predictive capabilities of amorphization models, and residual damage after regrowth are analyzed.