During the last decade, considerable progress has been made in understanding the properties and behavior of the vacancy V and self-interstitial I in silicon (Si) and germanium (Ge) crystals. This is to a large extent due to the maturing of density functional theory (DFT) calculation techniques and the increase of computing power enabling to calculate not only the formation and migration energies of V and I, but also the interaction with impurities and with crystal surfaces. Furthermore, the impact of internal and external stress on formation and migration enthalpies of both intrinsic point defects has been clarified recently. In this paper an overview is given on recent assessments on the properties of intrinsic point defects in Si and Ge, and on the useful application of DFT calculations for the control and engineering of intrinsic point defects in Si and Ge single crystal growth from a melt.