In this talk, I will present progress on three projects in my group that are unified by their need for strained or lattice-mismatched growth. The first topic is molecular beam epitaxy (MBE) of metamorphic InGaP and GaAsP for solar cells. Our interest in metamorphic InGaP stems from the fact that its bandgap can be tuned to values as high as ~2.2 eV. Such high bandgap materials will be necessary for multi-junction solar cells to reach 60% efficiency, but mismatched epitaxy is required since the compositions of interest do not possess the same lattice constant as common substrate materials. In contrast, metamorphic GaAsP is needed as a top junction on Si for high-efficiency, lowcost applications. I will discuss how control over extended defects in these materials led to our demonstration of high open-circuit voltage InGaP and GaAsP cells on both GaAs and GaP substrates. Next, I will discuss the strain-driven growth and luminescence properties of InGaAs quantum dots (QDs) on GaP. Since GaP is nearly lattice-matched to Si, these dots represent a new approach to efficient light emission on Si. Results on incorporation of InGaAs/GaP QDs into light-emitting diodes and photonic crystal cavities will be presented. The third topic is my group’s recent discovery that dislocation-free, tensile-strained nanostructures can be grown on (110) and (111) substrates. This result is unusual, since self-assembled island growth is typically driven by compressive strain on the (001) surface. I will present our analysis of these findings in terms of dislocation kinetics, as well as future prospects for tensile QDs.