Exploring QCD in ultraperipheral collisions with production of leading J/psi meson

We review several possibilities for probing QCD dynamics in ultraperipheral heavy ion collision with $J/\psi $ production. We argue that rapidity gap events in $\gamma p$ and $\gamma A$ scattering allow to study the BFKL dynamics, as well as dynamics of propagation of small dipoles through nuclei. At the same time coherent and quasielastic $J/\psi$ production in $\gamma A$ scattering provide a unique information about gluon shadowing at small x and moderate virtualities.