Though there is no doubt about the importance of turbulent flow phenomena in engineering systems, the reliable prediction of turbulence remains an elusive goal. Direct numerical simulation of turbulent flows is possible at sufficiently low Reynolds numbers, while large-eddy simulation may be applied in the higher Reynolds number range of engineering importance. A six-month research programme organized in 1999 by the Isaac Newton Institute, Cambridge University, brought together experts from different communities to develop understandings of practical and fundamental problems in turbulence. This collection of papers, from one of the symposia held as part of the research programme in conjunction with ERCOFTAC, presents progress in the use of direct and large-eddy simulation. Describing simulations of turbulence and transition and approaches to the mathematics and physics of subgrid closures, the volume gives a clear overview of the status of this research area and its practical applications.