  We describe how the usual supercharges of extended supersymmetry may be {\it
twisted} to produce a BRST-like supercharge $Q$. The usual supersymmetry
algebra is then replaced by a twisted algebra and the action of the twisted
theory is shown to be generically $Q$-exact. In flat space the twisting
procedure can be regarded as a change of variables carrying no physical
significance. However, the twisted theories can often be transferred to the
lattice while preserving the twisted supersymmetry. As an example we construct
a lattice version of the two-dimensional supersymmetric sigma model.
