  In cosmology numerical simulations of structure formation are now of central
importance, as they are the sole instrument for providing detailed predictions
of current cosmological models for a whole class of important constraining
observations. These simulations are essentially molecular dynamics simulations
of N (>> 1), now up to of order several billion) particles interacting through
their self-gravity. While their aim is to produce the Vlasov limit, which
describes the underlying (``cold dark matter'') models, the degree to which
they actually do produce this limit is currently understood, at best, only very
qualitatively, and there is an acknowledged need for ``a theory of discreteness
errors''. In this talk I will describe, for non-cosmologists, both the
simulations and the underlying theoretical models, and will then focus on the
issue of discreteness, describing some recent progress in addressing this
question quantitatively.
