Nonequilibrium steady states in driven diffusive systems exhibit many
features which are surprising or counterintuitive, given our experienc
e with equilibrium systems. We introduce the prototype model and revie
w its unusual behavior in different temperature regimes, from both a s
imulational and analytic view point We then present some recent work,
focusing on the phase diagrams of driven bi-layer systems and two-spec
ies lattice gases. Several unresolved puzzles are posed. (C) 1998 Else
vier Science B.V. All rights reserved.