Topology optimization (TO) has become a core computational paradigm for structural design by defining optimality through physics-based objectives and constraints. However, practical engineering design often involves incomplete and imperfect physical modeling due to multi-physics coupling, manufacturing uncertainty, and computational constraints, leaving critical design factors insufficiently captured in purely physics-driven formulations. In parallel, data-driven and generative methods have enabled rapid topology generation and intent-aware design exploration, yet often weaken explicit optimality guarantees. This review argues that these seemingly divergent developments can be organized under a unified information–physics perspective. We term this emerging field Topology Optimization Informatics (TOI): optimal structural design is obtained through the joint modeling and optimization of physical laws and design-relevant information. We first summarize the integration of artificial intelligence (AI) and TO into two major paradigms: AI-based one-shot TO, which learns mappings or distributions of near-optimal designs from data and prioritizes fast generation and diversity, and AI-enhanced iterative TO, which embeds learning-based modules into the classical solver-in-the-loop pipeline while keeping the underlying governing equations unchanged. Finally, we show that traditionally separate tasks—design control, computational acceleration, and fidelity enhancement—can be interpreted as different manifestations of information–physics co-modeling within a single optimization framework, thereby clarifying their connections and design implications and outlining opportunities for semantic- and data-enabled next-generation structural design.