  We investigate the photoproduction of $\rho$ mesons in ultraperipheral heavy
ion collisions at RHIC and LHC energies in the dipole approach and within two
phenomenological models based on the the Color Glass Condensate (CGC)
formalism. We estimate the integrated cross section and rapidity distribution
for meson production and compare our predictions with the data from the STAR
collaboration. In particular, we demonstrate that the total cross section at
RHIC is strongly dependent on the energy behavior of the dipole-target cross
section at low energies, which is not well determined in the dipole approach.
In contrast, the predictions at midrapidities at RHIC and in the full rapidity
at LHC are under theoretical control and can be used to test the QCD dynamics
at high energies.
