  Nuclear effects for J/Psi 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-cbar 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-cbar 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/Psi 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-cbar 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/Psi is found to be a clean and
sensitive tool measuring the transport coefficient characterizing the dense
matter created in AA collisions. RHIC data for pT dependence of J/Psi
production in nuclear collisions are well explained with the low value of the
transport coefficient q_0-hat<0.5 GeV^2/fm.
