An appealing approach to manufacturing future generation nanoscale devices envisioned for electronic, magnetic and photonic applications is to exploit the natural tendency of small material clusters to self-organize into well-defined patterns. While strain- driven self-assembly is widely viewed as a promising technique for patterning at the nanoscale, to follow this approach and create structures in a desired manner, a reliable means to engineer the characteristic size and shapes that the clusters adopt during self- assembly is essential. Motivated by a significant potential technological impact, a systematic elucidation of how long-range elastic interactions couple with surface and bulk thermodynamics and kinetics to control shape, size and compositional patterns assumes a paramount importance. The work presented here describes a detailed analysis of evolution of morphological and compositional patterns in various strain-driven self-assembled systems. The examples include alloy quantum dots and 2D patterns such as surface stress domains and epitaxial nanowires.