Abstract Nuclear effects for J / Ψ production in pA collisions are controlled by the coherence and color transparency effects. Color transparency onsets when the time of formation of the charmonium wave function becomes longer than the inter-nucleon spacing. In this energy regime the effective break-up cross section for a c ¯ c dipole depends on energy and nuclear path length, and agrees well with data from fixed target experiments, both in magnitude and energy dependence. At higher energies of RHIC and LHC coherence in c ¯ c pair production leads to charm quark shadowing which is a complement to the high twist break up cross section. These two effects explain well with no adjusted parameters the magnitude and rapidity dependence of nuclear suppression of J / Ψ observed at RHIC in dAu collisions, while the contribution of leading twist gluon shadowing is found to be vanishingly small. A novel mechanism of double color filtering for c ¯ c dipoles makes nuclei significantly more transparent in AA compared to pA collisions. This is one of the mechanisms which make impossible a model independent “data driven” extrapolation from pA to AA. This effect also explains the enhancement of nuclear suppression observed at forward rapidities in AA collisions at RHIC, what hardly can be related to the produced dense medium. J / Ψ is found to be a clean and sensitive tool measuring the transport coefficient characterizing the dense matter created in AA collisions. RHIC data for p T dependence of J / Ψ production in nuclear collisions are well explained with the low value of the transport coefficient q ˆ 0 < 0.5 GeV 2 / fm .