ABSTRACTThe transformations that take place in late‐type galaxies in the environment of rich clusters of galaxies at z = 0 are reviewed. From the handful of late‐type galaxies that inhabit local clusters, whether they were formed in situ and survived as such, avoiding transformation or even destruction, or if they are newcomers that have recently fallen in from outside, we can learn an important lesson on the latest stages of galaxy evolution. We start by reviewing the observational scenario, covering the broadest possible stretch of the electromagnetic spectrum, from the gas tracers (radio and optical) to the star formation tracers (UV and optical), the old star tracers (near‐IR), and the dust (far‐IR). Strong emphasis is given to the three nearby, well‐studied clusters Virgo, A1367, and Coma, which are representative of different evolutionary stages, from unrelaxed and spiral‐rich (Virgo) to relaxed and spiral‐poor (Coma). We continue by providing a review of models of galaxy interactions that are relevant to clusters of galaxies. Prototypes of various mechanisms and processes are discussed, and their typical timescales are given in an a. Observations indicate the presence of healthy late‐type galaxies falling into nearby clusters individually or as part of massive groups. More rare are infalling galaxies belonging to compact groups, where significant preprocessing might take place. Once they have entered the cluster, they lose their gas and quench their star formation activity, becoming anemic. Observations and theory agree in indicating that the interaction with the intergalactic medium is responsible for the gas depletion. However, this process cannot be the origin of the cluster lenticular galaxy population. Physical and statistical properties of S0 galaxies in nearby clusters and at higher redshift indicate that they originate from spiral galaxies that have been transformed by gravitational interactions.