The role of cluster assembly processes in driving the evolution of galaxies as a function of galaxy mass and/or environment is still an open issue. By studying the distributions of galaxy populations of different spectral type in the projected phase space, we can piece together a likely scenario for the galaxy assembly history of galaxy clusters and constrain the physical mechanisms involved in the transformation of star forming field galaxies to passive cluster galaxies. I will present results for four galaxy clusters with different dynamical status: MACS J1206.2-0847, an almost relaxed system at z~0.44, MACS J0416.1-2403 and RXJ2248-4431 (i.e. Abell S1063), two clusters with complex merging structures at z~0.40 and z~0.35, respectively, and Abell 209, a cluster presently undergoing strong dynamical evolution at z~0.21. To perform this analysis I take advantage from the dataset of the CLASH-VLT survey, which provides an unique combination of photometric coverage over a wide wavelength range [0.2-1.6] mu, from the HST observations and SUBARU/WFI, and wide-field VLT-VIMOS and integral-field VLT-MUSE spectroscopy yielding ~600, 900, 1200 and 1100 cluster members for MACS J1206.2-0847, MACS J0416.1-2403, RXJ2248- 4431 and Abell209, respectively. This large spectroscopic samples of cluster galaxies allow to link the cluster dynamical substructure with distinct galaxy populations, thus going beyond the simplistic concept of radial accretion and following cluster formation through their building blocks.