Strained-layer heteroepitaxy has evolved as a novel method for direct synthesis of self-assembled quantum dots based on the Stranski-Krastanow growth mode where nano-scale 3D islands spontaneously form on the surface of a thin wetting layer. In multilayers, the buried dots tend to influence the dot nucleation in the subsequent layers due to the existence of long range elastic interactions. As a result, vertical and lateral correlations within the dot ensembles are formed, which can lead to a lateral ordering and size homogenization of the dots. Here, it is shown that for various materials systems, different correlated structures are formed depending on the elastic anisotropy of the materials and depending on the growth orientation. As a most prominent example, in IV-VI semiconductor dot superlattices a nearly perfect lateral ordering and a fcc-like ABCABC... vertical stacking of the dots is obtained, and the spacing between the dots can be tuned continuously just by changing of the superlattice period. The basic mechanisms and the limits of the ordering process is discussed on the basis of theoretical calculations and Monte Carlo growth simulations.