Scientific simulation, which provides a natural bridge between theory and experiment, is an essential tool for understanding complex plasma behaviour. Recent advances in simulations of magnetically confined plasmas are reviewed in this paper, with illustrative examples, chosen from associated research areas such as microturbulence, magnetohydrodynamics and other topics. Progress has been stimulated, in particular, by the exponential growth of computer speed along with significant improvements in computer technology. The advances in both particle and fluid simulations of fine-scale turbulence and large-scale dynamics have produced increasingly good agreement between experimental observations and computational modelling. This was enabled by two key factors: (a) innovative advances in analytic and computational methods for developing reduced descriptions of physics phenomena spanning widely disparate temporal and spatial scales and (b) access to powerful new computational resources. Excellent progress has been made in developing codes for which computer run-time and problem-size scale well with the number of processors on massively parallel processors (MPPs). Examples include the effective usage of the full power of multi-teraflop (multi-trillion floating point computations per second) MPPs to produce three-dimensional, general geometry, nonlinear particle simulations that have accelerated advances in understanding the nature of turbulence self-regulation by zonal flows. These calculations, which typically utilized billions of particles for thousands of time-steps, would not have been possible without access to powerful present generation MPP computers and the associated diagnostic and visualization capabilities. In looking towards the future, the current results from advanced simulations provide great encouragement for being able to include increasingly realistic dynamics to enable deeper physics insights into plasmas in both natural and laboratory environments. This should produce the scientific excitement which will help to (a) stimulate enhanced cross-cutting collaborations with other fields and (b) attract the bright young talent needed for the future health of the field of plasma science.