Future wireless networks will be required to provide more wireless services at higher data rates and with global coverage. However, existing homogeneous wireless networks, such as cellular and satellite networks, may not be able to meet such requirements individually, especially in remote terrain, including seas and mountains. One possible solution is to use diversified wireless networks that can exploit the inter-connectivity between satellites, aerial base stations (BSs), and terrestrial BSs over inter-connected space, ground, and aerial networks. Hence, enabling wireless communication in one integrated network has attracted both the industry and the research fraternities. In this work, we provide a comprehensive survey of the most recent work on hybrid satellite–terrestrial networks (HSTNs), focusing on system architecture, performance analysis, design optimization, and secure communication schemes for different cooperative and cognitive HSTN network architectures. Different key technologies are compared. Based on this comparison, several open issues for future research are discussed.