  We present results from recent investigations of diffractive vector meson
production using the ZEUS detector at HERA. These consist of measurements of
rho production in the region of photon virtuality 0.25 < Q^2 < 0.85 GeV^2, of
rho, phi, and J/psi production for values of the momentum transfer to the
proton 0.3 < |t| < 4.0 GeV^2, and of elastic J/psi production both in
photoproduction and for Q^2 > 2 GeV^2.
