Satellite constellations are transforming space systems from isolated spacecraft into networked, software-defined platforms capable of on-orbit perception, decision making, and adaptation. Yet much of the existing AI studies remains centered on single-satellite inference, while constellation-scale autonomy introduces fundamentally new algorithmic requirements: learning and coordination under dynamic inter-satellite connectivity, strict SWaP-C limits, radiation-induced faults, non-IID data, concept drift, and safety-critical operational constraints. This survey consolidates the emerging field of on-orbit space AI through three complementary paradigms: (i) {federated learning} for cross-satellite training, personalization, and secure aggregation; (ii) {multi-agent algorithms} for cooperative planning, resource allocation, scheduling, formation control, and collision avoidance; and (iii) {collaborative sensing and distributed inference} for multi-satellite fusion, tracking, split/early-exit inference, and cross-layer co-design with constellation networking. We provide a system-level view and a taxonomy that unifies collaboration architectures, temporal mechanisms, and trust models. To support community development and keep this review actionable over time, we continuously curate relevant papers and resources at https://github.com/ziyangwang007/AI4Space.