This paper reviews the critical ionization velocity (CIV) phenomenon, with inclusion of recent research. CIV, suggested by Alfv¿n in 1954 as part of a larger cosmological theory accounting for the formation of the solar system, is controversial in that laboratory and space experiments to confirm its validity have yielded conflicting results. Theoretical analysis has suggested that the driving mechanism for CIV is some form of beam-plasma instability, such as the lower hybrid instability, which leads to rapid energization of ambient electrons so that they gain enough energy to ionize the beam of neutral atoms by electron impact. The newly created beam ions energize the instability, thus fostering a cyclic process that may lead to an avalanche ionization. Because the implications of this process, if correct, are widespread, it has become important to establish a theoretical framework for its presence and its occurrence. This framework includes a variety of microscopic chemical and physicochemical processes, such as line excitation, formation of metastable states by electron impact, ionization of metastable states by electron impact, and ion-electron recombination in the case of molecular ions. These reactions may occur in CIV experiments both in the laboratory and in space. Numerical computer models have been able to not only simulate CIV but also reveal details in nonlinear plasma evolution together with electron impact ionization of the neutral particles. Theories, laboratory experiments, and computer simulations have all shown CIV as feasible and reasonably understood, although all CIV experiments in space have yielded negative results with perhaps three exceptions. In the CIV experiments in space, not only the ionization yields were low, but also non-CIV processes such as charge exchange, associative ionization, and stripping ionization may have occurred and may be easily mistaken as CIV. We also discuss the conditions under which the laboratory and the space experiments are carried out and highlight the differences, some of which may explain the different results. ¿ 2001 American Geophysical Union