The scientific understanding of lattice-mismatched epitaxy has lead to a third era in the applications of epitaxy. Epitaxy was applied in applications benefiting from lattice-matched materials, and has migrated to applications with mild lattice-mismatch, such as the SiGe HBT and the InGaAs pHEMT. Today, we are able to create relaxed lattice constants that have significant lattice-mismatch with respect to bulk substrate, and in turn use those lattice constants to create extremely high levels of strain in new and conventional materials. In this talk, we will review the general principles of strain-relaxed epitaxy and show how new SiGe templates on Si have extended the electron and hole mobility in SiGe materials to unforeseen enhancements. Such enhancements promise to increase the current drive in MOSFET transistors at a time when smaller transistors are losing their driving efficacy as scaling continues. We show that strained SiGe nanochannels are most likely shaping the vertical wavefunction of carriers, leading to the very high enhancements in mobility despite very high vertical fields. New structures that not only add strain but are further engineered for robust processing will be presented.