Modern CCD instrumentation has made it possible to obtain photometric and spectroscopic data on normal galaxies in clusters at redshifts up to nearly unity. In this paper we discuss a survey for such clusters and preliminary spectroscopic results for galaxies in a sample of 7 clusters near redshift 0.5, and another at z=0.75. The data clearly indicate strong evolution of a sizeable fraction of the cluster population, in the sense that there were many more “active” galaxies then than at the present epoch. The physical mechanism responsible for the activity is as yet uncertain, but we discuss what we consider a likely candidate. The evolution of the “passive”, red population is sufficiently slow that strong constraints are placed on the rate of continuing star formation or, alternatively, on the formation epoch.