Basic processes responsible for the formation of quantum dot (QD) nanostructures occur on a large range of length and time scales. Understanding this complex phenomenon requires theoretical tools that span both the atomic-scale details of the first-principles methods and the more coarse-scale continuum approach. By discussing the time scale hierarchy of different elementary kinetic processes we emphasize several levels of constraint equilibrium of the system and elucidate pathways to reach corresponding stable or metastable states. Main focus is given to the InAs/GaAs material system which is the most advanced one for applying QDs in optoelectronics. First principles calculations of the potential energy surfaces by the density functional theory (DFT) gain the knowledge about potential minima corresponding to the preferred adsorption sites and barriers that govern the rates of diffusion, desorption, and island nucleation in both unstrained and strained systems. Based on these ab initio parameters, kinetic Monte Carlo (kMC) simulations have allowed a detailed theoretical description of GaAs/GaAs and InAs/InAs homoepitaxial growth and elucidated the nucleation and evolution of InAs islands on GaAs. A hybrid approach combining DFT calculations of the surface energies and continuum elasticity theory for the strain relaxation energy has given the equilibrium shape of InAs/GaAs QDs as a function of volume and explained the observed shape transitions. For the ensembles of strained QDs, the Fokker-Planck evolution equation has explained the formation of different types of metastable states in sparse and dense arrays, and the kMC simulations have proposed a tool to distinguish kinetically controlled and thermodynamically controlled QD growth. By continuum elasticity theory in elastically anisotropic semiconductor systems, transitions between vertically correlated and vertically anticorrelated growth of QD stacks has been explained, and yet another approach has been proposed to control the formation of complex nanoworlds.