I will present recent efforts to understand early cluster formation phases at z>2, the epoch of the peak star formation and black hole activity in the Universe, when the first giant dark matter halos were rapidly growing. Baryons falling into their deep potential wells took part to prodigiously vigorous activity of galaxy and black hole assembly. These phases are expected to be important to understand how we get to the formation of the dominant early type galaxy population and well relaxed hot gas atmospheres, as observed in local massive galaxy clusters. New observations with many facilities (e.g., ALMA, NOEMA, Herschel, VLA, HST and Keck) of several dense structures at z=2 to 3 provide new insights into these problematics. A large variety of forthcoming facilities (Euclid, Athena, SKA, JWST, VLT-MOONS, VLT-BlueMUSE, and the ELTs) hold the promise to revolutionise this field in the coming decades, and I will briefly mention some of the expected applications.