The growth of heteroepitaxial structures remains a critical scientific and technological challenge. From semiconductors to superconductors, advanced devices and applications require thin films with well-controlled lattice parameter and orientation on substrates of many different types. In addition, misfit stress and surface energy differences in heterolayers can be used to drive the formulation of nanoscale structures. Quantum dots and metallic nanoparticles with unique and useful properties can be made that assemble themselves during the deposition process. This compilation of papers reflects, both experimentally and theoretically, the wide range of topics in this area of research - from the early stages of epilayer growth and self assembly, to the mechanisms and late stages of strain relaxation through both island formation and dislocation injection. Topics include: early stages and fundamental processes of heteroepitaxy; heteroepitaxy and self assembly; stress relaxation; stress and islanding; modifying and controlling growth; quantum dots - applications and properties; relaxation, morphology and composition modulations and heteroepitaxy in metals and oxides.