The development of strain relaxation in lattice-mismatched semiconductor nanowire heterostructures is reviewed. Theoretical predictions for critical geometries for axial and core–shell structures are summarized and compared to experimental reports. All agree that nanowires can accommodate a greater elastic strain than is commonly seen with planar interfaces. Large mismatch as high as 10% has been elastically accommodated consistent with theoretical predictions. Elastically strained nanowire examples predominate, likely since nucleation is otherwise inhibited. A (maximum) critical radius is observed for epitaxial growth directly onto lattice-mismatched substrates. The few examples where strain relaxation via dislocations or roughening has been observed have been reported for core–shell geometries.