The generic heterogeneous effect of foreign particles on three dimensional nucleation was examined both theoretically and experimentally. It shows that the nucleation observed under normal conditions includes a sequence of progressive heterogeneous processes, characterized by different interfacial correlation function f(m,x)s. At low supersaturations, nucleation will be controlled by the process with a small interfacial correlation function f(m,x), which results from a strong interaction and good structural match between the foreign bodies and the crystallizing phase. At high supersaturations, nucleation on foreign particles having a weak interaction and poor structural match with the crystallizing phase (f(m,x)-->1) will govern the kinetics. This frequently leads to the false identification of homogeneous nucleation. Genuine homogeneous nucleation, which is the up-limit of heterogeneous nucleation, may not be easily achievable under gravity. In order to check these results, the prediction is confronted with nucleation experiments of some organic and inorganic crystals. The results are in excellent agreement with the theory.