In this paper, we succinctly delineate the contemporary status and prospective developmental trends of teraliertz inter-satellite networks (THz-ISNs). Leveraging a layered network architecture framework, we deliver a brief overview of THz-ISNs across the physical, media access control, and network layers. This brief review yields systematic comprehension and insightful perspectives for cross-layer design in THz-ISNs. Furthermore, considering the evolution of wireless networks and artificial intelligence, we foresee future developmental trends for THz-ISNs. Encompassing advancements such as the reconfigurable intelligent surface, semantic communications, and intent-driven network control and management, we offer valuable insights into the future research directions for THz-ISNs.