Video foundation models have advanced rapidly in understanding and generating visual sequences, while video world models seek to capture the underlying dynamics of the world they depict. Despite their different objectives, both concern the relationship between video observations and an evolving world. This survey adopts world modeling as a unifying lens for examining these developments. Viewing an observed video as a partial, lossy, and temporally ordered projection of a latent temporal world, we organize the literature around four complementary operations: reading infers world properties from observed video; writing synthesizes video from specified or learned world conditions; sharing integrates understanding and generation through common modeling mechanisms; and interacting predicts and updates world states under actions and evolving observations. This perspective distinguishes temporal coherence in observed or generated sequences from consistency in the underlying world state. Across tasks, representations, models, datasets, and benchmarks, we trace a shift in emphasis from clip-level recognition and perceptual fidelity toward persistent state, controllable evolution, physical and causal validity, and evaluation grounded in interaction and downstream decisions, and we distill the open challenges that follow.

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