Epitaxial silicides belong to a special class of silicides which exhibit a definite orientation relationship with respect to the silicon substrate. A silicide is expected to grow epitaxially on silicon if the crystal structures are similar and the lattice mismatch between them is small. The impetus for the study of epitaxial silicides mainly stemmed from several favorable characteristics of epitaxial silicides in comparison with their polycrystalline counterparts. It now appears that almost all transition-metal silicides can be grown epitaxially to a certain extent on silicon. In this report, theories for the epitaxial growth of silicides are first discussed. The formation and characterization of epitaxial silicides by different techniques are described. Epitaxial growth in various metal/Si systems is summarized. Several recent developments in the growth of transition-metal silicides on silicon are described. Factors influencing the growth of epitaxy are examined. Properties and device applications of epitaxial silicides are addressed.