Compliant substrates allow a new approach to the growth of strained epitaxial layers, in which part of the strain is accommodated in the substrate. In this article compliant substrates are discussed and a new compliant substrate technology based on bonded thin flim substrates is introduced. This technology has several advantages over previously published methods, including the ability to pattern both the top and bottom of the material. A new concept enabled by this compliant substrate technology, strain modulated epitaxy, will be introduced. Using this technique, the properties of the semiconductor material can be controlled laterally across a substrate. Results of two experiments are presented in which low composition InxGa1-xAs was grown by molecular beam epitaxy on GaAs compliant substrates at thicknesses both greater than and less than the conventional critical thickness. It was found that for t > tc, there was an inhibition of defect production in the epitaxial films grown on the compliant substrates as compared to those grown on conventional reference substrates. For t < tc, photoluminescence and x-ray diffraction show the compliant substrates to be of excellent quality and uniformity as compared to conventional substrates.