The excellent physical properties of diamond make it one of the most promising semiconductor materials for the next generation. At present, heteroepitaxy based on microwave plasma chemical vapor deposition may be the best method for preparing large-scale single crystal diamond in the future. In the past three decades, some progress has been made in the heteroepitaxial growth of single crystal diamond on iridium-based composite substrates, especially in recent years, the growth of large-scale single crystal diamond of more than 2 inch has been realized. This paper summarizes the various substrates used for diamond heteroepitaxy, briefly introduces bias-enhanced nucleation on heterogeneous substrates, and details the most successful iridium/oxide, iridium/oxide layer/silicon composite substrates. In the end, the problems existing in diamond heterogeneous substrates and heteroepitaxy are summarized, and some possible solutions are given.