Templated growth for the fabrication of semiconductor nanostructures such as quantum dots and lattice-mismatched structures has been employed in this study. Self assembly of block copolymers (BCP) has been exploited to create a regular array of nanoscale patterns on a substrate to generate the growth template. These patterned templates were used for the selective area growth of pseudomorphic quantum dots, allowing for precise control over the dot size and spatial distribution. Strain relaxation in lattice-mismatched structures grown past the pseudomorphic limit was also studied. Analysis of the grown structures suggests that this approach using block copolymer templating followed by selective growth can be used for defect reduction in lattice-mismatched materials.