State, Action, and Transition: An Application-Oriented Bottleneck-Driven Survey of World Models

World models represent environments and predict how their states evolve under interventions. Their use in generative simulation and interactive environments, autonomous driving, and robotics and embodied control is growing, yet application validation remains fragmented across model families. Using the relation st+1∼pθ(⋅∣st,at), this review organizes the field around state representation, action representation, and transition modeling. We compare visual and geometric states with object-centric or belief/latent organization; semantic, hierarchical, latent, and executable actions; and autoregressive, diffusion-based, predictive latent, explicit-simulation, and learned–physics hybrid transitions. Across the three applications, we connect these choices to identity drift, non-executable plans, unsafe multimodal forecasts, long-horizon instability, and sim-to-real degradation. We then link each failure to six diagnostic dimensions: perceptual fidelity, physical validity, action consistency, rollout stability, calibration, and decision utility. The synthesis provides a cross-application engineering matrix and motivates Active Intervention Loops, Physical Laws Internalization, and Progressive Structural Integration. It identifies the State–Action–Transition commitments that shape application suitability and separates visual plausibility from evidence of interactive or deployment readiness.