  This is our current research perspective on models providing insight into
statistical mechanics. It is necessarily personal, emphasizing our own interest
in simulation as it developed from the National Laboratories' work to the
worldwide explosion of computation of today. We contrast the past and present
in atomistic simulations, emphasizing those simple models which best achieve
reproducibility and promote understanding. Few-body models with pair forces
have led to today's "realistic" simulations with billions of atoms and
molecules. Rapid advances in computer technology have led to change.
Theoretical formalisms have largely been replaced by simulations incorporating
ingenious algorithm development. We choose to study particularly simple, yet
relevant, models directed toward understanding general principles. Simplicity
remains a worthy goal, as does relevance. We discuss hard-particle virial
series, melting, thermostatted oscillators with and without heat conduction,
chaotic dynamics, fractals, the connection of Lyapunov spectra to
thermodynamics, and finally simple linear maps. Along the way we mention
directions in which additional modelling could provide more clarity and yet
more interesting developments in the future.
