Machine learning is increasingly used for spacecraft telemetry monitoring, fault diagnosis, health assessment, mission planning, visual navigation, and execution review. In space missions, explainability is a foundation of trustworthy artificial intelligence because engineers must understand the evidence behind model outputs before incorporating them into operational decisions. Explainability should therefore transform internal model computations into evidence that engineers can inspect during mission execution and integrate into an intuitive mental model of spacecraft state, model rationale, and possible action consequences. Such evidence may include channel–time patterns, rule paths, prototype events, active constraints, or subsystem propagation hypotheses. It must remain traceable to the model, consistent with spacecraft modes and physical constraints, and usable in reviewable decisions. This review distinguishes the mechanism that generates an explanation from the strength of its spacecraft validation. It examines interpretable-by-design models and six post-hoc families, separating direct spacecraft evidence from methods transferable from adjacent domains. A V0–V5 scale describes evidence ranging from generic experiments to measured mission-support benefit. Finally, the review discusses the Open-Box method and examines how exact and consistent regional representations may be relevant to piecewise-linear network families within verified operating regions.