It is now possible to grow high-quality strained-layer superlattices, in which individual layers are composed of semiconductor materials which would normally have significantly different lattice constants. Strained structures open new possibilities for band-structure engineering and applications, but place even higher demands on crystal growth techniques.In this Review, we first describe some of the growth that has been achieved and the theoretical and experimental limits on good quality growth. We then discuss in detail the electronic structure of strained quantum wells, and in particular the possibility of valence band engineering in strained layers. Axial strain splits the degeneracy of the light-and heavy-hole zone centre states, accessing a range of subband structures, including the possibility of the highest band being light-hole-like, and of holes with electron-like zone centre masses. We next describe the experimental evidence confirming such subband structures.This strain-based band engineering suggests new device applications, including high hole mobility transistors and low threshold current, longwavelength lasers. We review what has been achieved in respect of the main proposed device applications to date. Strained layers are also of interest for the new materials combinations which they allow. We briefly overview some of the materials-based advantages, and conclude that strained layers will continue to attract significant attention.