The self assembly of quantum dots by heteroepitaxy of lattice-mismatched semiconductors is based on elastic energy relaxation, which spontaneously occurs at the growth front when the largest atoms in the crystal cluster together. Because a larger covalent radius is related to weaker bonds, and this is in turn fundamentally related to smaller bandgaps, the formation of quantum dots leads to a confinement potential for electrons and/or holes. This effect has applications ranging from ultralow threshold diode lasers to highly efficient solar cells and usually requires the stacking of multiple quantum dots. The number of layers is limited by the stress accumulated during growth due to the larger covalent radius of the atoms that constitute the quantum dots. This accumulated stress can be relieved by introducing in the epitaxial layers compensating atomic species with a smaller covalent radius, enabling a reduction of spacer layer thickness. In the limit of sub-nanometer spacer thickness, the quantum dots, which have a tendency to line up vertically, fuse into a quantum post. The current efforts to optimize the properties of strain balanced quantum dot stacks and quantum posts are reviewed.