The physics of the growth mechanisms, characterization of epitaxial structures and device properties of GaAs and other compound semiconductors on Si are reviewed in this paper. The nontrivial problems associated with the heteroepitaxial growth schemes and methods that are generally applied in the growth of lattice mismatched and polar on nonpolar material systems are described in detail. The properties of devices fabricated in GaAs and other compound semiconductors grown on Si substrates are discussed in comparison with those grown on GaAs substrates. The advantages of GaAs and other compound semiconductors on Si, namely, the low cost, superior mechanical strength, and thermal conductivity, increased wafer area, and the possibility of monolithic integration of electronic and optical devices are also discussed.