  Evolution in the merger rate as a function of redshift is in principle the
key observable testing hierarchical models for the formation and evolution of
galaxies. However, in practice, direct measurement of this quantity has proven
difficult. In this opening review I outline the current best estimates for the
merger rate as a function of cosmic epoch, focussing mostly upon recent
advances made possible by deep ground-based redshift surveys and morphological
studies undertaken with HST. I argue that a marriage of these techniques, in an
attempt to determine the space density of mergers amongst the abundant
morphologically peculiar population at high redshifts, is probably the most
promising currently-available avenue for determining the prevalence of mergers
at high redshifts. However, resolved kinematical studies, which seem set to
become available in the next few years, are probably the best hope for a
definitive determination of the space density of mergers at high redshifts.
