  Exclusive vector meson production reactions such as $Au + Au \to Au + Au +
V$, where $V=\rho, \omega, \phi$ or $J/\psi$ can proceed through photon-Pomeron
and photon-meson interactions. Photons from the electromagnetic field of one
nucleus interact coherently with the other nucleus. Photonuclear cross sections
are scaled from $\gamma p$ data, and convoluted with the photon spectrum to
find the exclusive rates.
  The cross sections at the RHIC and LHC heavy ion colliders are huge, 10% of
the total hadronic cross section at RHIC, and 50% at LHC. These accelerators
may be useful as vector meson factories. With iodine beams at RHIC, 640 $\rho$
are produced each second (10^{10}/year); with calcium at the LHC the rate is
240 kHz. The $\phi$ rates are 39 Hz at RHIC and 15 kHz at LHC, while the
$J/\psi$ rate is 0.3 Hz at RHIC and 780 Hz at the LHC.
  Because of the coherent couplings, the reactions kinematics are similar to
coherent two-photon interactions; we discuss the interplay between the two
reactions.
