  In the first part of the paper a general notion of sampling expansions for
locally compact groups is introduced, and its close relationship to the
discretisation problem for generalised wavelet transforms is established. In
the second part, attention is focussed on the simply connected nilpotent
Heisenberg group $\HH$. We derive criteria for the existence of discretisations
and sampling expansions associated to lattices in $\HH$. Analogies and
differences to the sampling theorem over the reals are discussed, in particular
a notion of bandwidth on $\HH$ will figure prominently. The main tools for the
characterisation are the Plancherel formula of $\HH$ and the theory of
Weyl-Heisenberg frames. In the last section we compute an explicit example
