With the evolution of fifth-generation (5G) to sixth-generation (6G) communication systems, the utilization of spectrum resources faces incremental challenges. Integrated sensing and communication (ISAC) technology, as a crucial element in 6G technology, is expected to enhance energy efficiency and spectrum utilization efficiency by integrating radar and communication signals, achieving environmental awareness, and enabling scene interconnection. Simultaneously, to realize the vision of seamless coverage in 6G, research on integrated satellite-terrestrial communication has been prioritized. To integrate the advantages, ISAC for integrated satellite–terrestrial networks (ISTNs) in 6G has emerged as a potential research direction. This paper offers an extensive overview of the present state of key technologies for ISAC and the development of ISTNs. Meanwhile, with a focus on the ISTN-oriented 6G ISAC system, several hotspot topics, including future application scenarios and key technological developments, are outlined and demonstrated.