Originally, our work in this area was focussed on addressing fundamental questions concerning the microscopic basis of the Second Law of thermodynamics. More recently, my interest here has extended to an attempt to use simple microscopic models to understand the often complex behaviour of matter at the macroscopic level, in particular the nonequilibrium properties of fluids. The novel methods we have been investigating and applying include lattice gas and lattice Boltzmann automata, and dissipative particle dynamics.