Moving isotropic media are analyzed considering
superluminal phase velocities instead of the usual subluminal
regime. The following new effects arise: i) a complex aberration,
i.e., angles that are complex in the proper frame can correspond
to real angles in the lab frame; ii) Cerenkov effect occurs
although the usual condition associated with this effect, in which
the relative phase velocity is below the velocity between frames,
is not verified. Dispersion and losses are mandatory in order to
respect causality, therefore, a Lorentz causal dispersive model is
considered. We show that losses play a very important role in
the superluminal regime. Without losses the predicted effects
could occur for non-relativistic velocities between frames.