As Moore′s law is coming to an end,and the continuous pursuit of multi-functional integration,high density integration,small volume weight,low power consumption,large bandwidth,low delay,and so on,heterogeneous integration of functional devices and chips of various compound semiconductor material systems (such as GaN,InP,SiC,etc.) with chips of CMOS integrated circuit is beginning,which will bring a new revolution in the post Moore era.The silicon-based heterogeneous integration is also regarded as the technical platform for the development of the next generation integrated microsystems.The latest developments in the heterogeneous integration of compound semiconductor materials (or chips) with silicon semiconductor materials (or chips) in the field of RF microelectronics and silicon photonics are reviewed in the article,so as to provide domestic researchers with a more comprehensive understanding of the progress abroad.