We report on the results of a large program conducted mainly with the Very Large Telescope to search for proto-clusters of galaxies near powerful radio galaxies at 2< z <5.2 and simultaneously investigate the nature of giant Lyα nebulae centered on massive radio galaxies. Deep narrow- and broad-band images of eight radio galaxies and their environments were obtained, with subsequent spectroscopy to acquire redshifts for the candidate Lyα emitters. In at least five fields, an overdensity of Lyα emitters is found near the radio galaxy, with a significant clustering in redshift space of the emitters. Based on the estimated masses and the volume densities, we argue that the observed structures are the likely progenitors of present-day massive (10¹⁵M_⊙ ) clusters of galaxies. A comparison with numerical experiments, simulating development of large scale structure in the Universe provides additional evidence for the hypothesis that these structures are forming massive clusters. Finally, we discuss physical properties of these clusters, cluster members and the central massive radio galaxies.