The transformations taking 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 recently infall 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, the star formation tracers, the old star tracers and the dust. Strong emphasis is given to the three nearby, well studied clusters Virgo, A1367 and Coma, representative of different evolutionary stages, from unrelaxed, spiral rich (Virgo) to relaxed, spiral poor clusters (Coma). We continue by providing a review of models of galaxy interactions relevant to clusters of galaxies. Prototypes of various mechanisms and processes are discussed and their typical time-scales are given in an Appendix. Observations indicate the presence of healthy late-type galaxies falling into nearby clusters individually or belonging to massive groups. More rare are infalling galaxies belonging to compact groups where significant pre-processing might take place. Once entered the cluster, they loose their gas and quench their star formation activity, becoming anemics. Observations and theory agree in indicating that the interaction with the intergalactic medium is responsible for the gas depletion. This process, however, cannot be at the origin of the cluster lenticular galaxy population. Physical and statistical properties of S0 in nearby clusters and at higher redshift, indicate that they originate from spiral galaxies transformed by gravitational interactions.

Review paper accepted for publication on PASP, high resolution version of the figures available on the GOLDMine webpage: http://goldmine.mib.infn.it/papers.html