This paper reviews recent considerable progress made in the last few years in understanding the behavior and properties of intrinsic point defects close to moving melt/solid Si interfaces during single crystal Si growth from a melt. The so called Voronkov criterion allows to determine whether the grown Si crystal is interstitial I-or vacancy V-rich. This criterion is written as the ratio G of the pulling rate v over the thermal gradient G at the interface. Crystals pulled with G above a critical value Gcrit are vacancy-rich while below Gcrit, they are interstitial-rich. Various expressions based on the intrinsic point defect thermal equilibrium concentration and diffusivity have been proposed to calculate Gcrit and are briefly discussed in this paper. Recently it was shown that the thermal stress at the interface and heavy doping with neutral and/or electrically active impurities, have a considerable impact on the intrinsic point defect balance and thus also on Gcrit. Furthermore, high energy barriers of formation energies of I and V around three or four atom layers from (001) free surface support a model in which the boundary conditions of the point defect concentrations at the surface in simulations can be set at fixed values. The situation is quite different for Ge single crystal pulling where the vacancy is always the dominant intrinsic point defect so that the Voronkov criterion cannot be applied. Prediction of vacancy cluster concentration/size distributions as a function of the pulling conditions is however still possible. The possibility of reaching Voronkov criterion conditions for Ge by doping with specific impurities is also discussed. Finally, impacts of stress and doping on self-diffusion in Si and Ge are evaluated with comparing the previous experimental results.