This paper presents a brief review of some recent work on the the use of wall compliance for laminar-flow control. Four main topics are covered. Firstly comparisons between theory and experiment for instability and transition in flat-plate boundary layers over compliant walls are considered. Good agreement is found for the Gaster experiments in water. But the theory does not corroborate the more recent experimental study of Lee et al. (T. Lee, M. Fisher, W.H. Schwarz, Journal of Fluid Mechanics 288 (1995) 37) in air. Secondly, the results of recent numerical simulations of the divergence instability are discussed. In agreement with experimental evidence it is found that the divergence onset speed for laminar flow is much higher than for turbulent flow. This implies that previous estimates of the onset speed based on potential flow are very conservative. Thirdly, the use of multiple-panel compliant walls for laminar-flow control is reviewed. Theory and numerical simulation strongly suggest that transition can be postponed to indefinitely high Reynolds numbers by the use of such walls. Lastly, recent work is reviewed on the effects of wall compliance on other instability mechanisms, such as inflexion-point instabilities and cross-flow vortices and absolute instabilities for the three-dimensional, rotating-disc boundary layer.