Mobile communication standards have been developed into a new era of B5G and 6G. In recent years, low earth orbit (LEO)satellites and space Internet have become hot topics. The integrated satellite and terrestrial systems have been widely discussed by indus-tries and academics, and even are expected to be applied in those huge constellations in con-struction. This paper points out the trends of two stages towards system integration of the terrestrial mobile communication and the sat-ellite communications: to be compatible with 5G, and to be integrated within 6G. Based on analysis of the challenges of both stages, key technologies are thereafter analyzed in detail,covering both air interface currently discussed in 3GPP for B5G and also novel network ar-chitecture and related transmission technolo-gies toward future 6G.