Heterogeneous catalytic epoxidation of functionalized olefins in the liquid phase has been reviewed focusing on catalyst performance and its interrelation with the crucial parameters of the catalytic systems. Efficient catalysts include supported and mixed oxides, framework-substituted ("redox") molecular sieves, layered-type materials, heterogenized homogeneous catalysts, and some others. Among the various substrates, allylic and homoallylic alcohols, and unsaturated carbonyl compounds have received most attention so far. The great variety of available catalysts enables selective epoxidation of most substituted olefins. The mechanistic understanding of heterogeneous catalytic epoxidation is still underdeveloped, rendering catalyst design rather empirical. A considerable potential for future development lies in the area of ''heterogenization" of successful homogeneous catalysts especially for asymmetric epoxidation. Crucial requirements in the development of heterogeneous catalytic epoxidation catalysts are, besides good catalytic performance and cheap oxidant, recyclability and resistance to leaching of the active component. Some of the examples shown in the literature do not fulfill the latter requirement.