The self-assembly of epitaxial quantum dots on (001) surfaces, driven by compressive strain, is a widely used tool in semiconductor optoelectronics. In contrast, the growth of quantum dots on (111) and (110) surfaces has historically been a significant challenge. In most cases the strain relaxes rapidly via dislocation nucleation and glide before quantum dots can form. In this paper, we discuss a method for the reliable and controllable self-assembly of quantum dots on both (111) and (110) surfaces, where tensile strain is now the driving force. By showing that tensile-strained self-assembly is applicable to several material systems, we demonstrate the versatility of this technique. We believe that tensile-strained self-assembly represents a powerful tool for heterogeneous materials integration, and nanomaterial development, with future promise for band engineering and quantum optics applications