Space missions increasingly depend on AI—from real-time, radiation-tolerant inference onboard satellites to ground-based analytics that fuse multi-sensor constellations with in-situ and economic data. This article provides a systems view of “Space-AI”: (1) constraints of computing in orbit; (2) onboard edge models for prioritization, compression, and autonomy; (3) mission planning and multi-satellite task allocation; (4) anomaly detection and fault management (FDIR); (5) communications and delay-tolerant networking; (6) Earth-observation (EO) analytics for agriculture, disasters, climate and maritime; (7) space situational awareness (SSA) and space-traffic management; (8) cybersecurity and certification for safety-critical AI; and (9) an edge-to-cloud reference architecture, KPIs, risks, and a rollout roadmap. The aim is a rigorous, implementation-ready blueprint—agnostic to specific vendors—that balances scientific value, operational safety, and economic return.