Silicon-based heterostructures have come a long way from the discovery of strain as a new and essential parameter for band structure engineering to the present state of electron and hole mobilities, which surpass those achieved in the traditional Si/SiO2 material combination by more than an order of magnitude and rapidly close up to the best III-V heteromaterials. Besides the inherent performance enhancement, undoubtedly the main attraction of high-mobility Si/SiGe and Si/SiC heterostructures is their basic compatibility with standard Si technologies. This unique combination of properties makes these materials the natural choice for future high performance VLSI circuits based on the contemporary MOSFET. It is the purpose of this contribution to critically review the most recent developments and the performance levels achieved to date in these material systems, to address problems related with device fabrication and process integration, and to discuss alternative routes that could circumvent the use of strain-adjusting epilayers, which are presently the bottleneck for an introduction of these promising materials into a production environment.