World models (WMs) provide a unified approach for modeling how environments evolve over time by learning predictive representations of states and observations. Recent advances in large-scale generative modeling and multimodal foundation models have substantially broadened their applicability across a wide range of interactive and multimodal domains; however, existing research remains fragmented across modeling paradigms, application domains, and evaluation protocols. This survey provides a systematic and in-depth review of WMs in artificial intelligence. Based on the world modeling paradigms of existing methods, we first categorize WMs into four branches with formal mathematical formulations: observation-level generative, latent space, reinforcement learning-based, and object-centric WMs. We further review a broad range of WM applications spanning robotics, autonomous driving, scientific discovery, game simulation, GUI-based agents, as well as interpretability and trustworthiness, and analyze benchmarks, new evaluation metrics, simulation platforms, and comparative results across WMs. Finally, we discuss key challenges, including long-horizon consistency, and generalization, and outline promising directions for future research. This survey provides an actively updated \href{https://github.com/JiahuaDong/Awesome-World-Models}{GitHub Repository} to track developments in WMs and aims to offer a unified reference for understanding, comparing, and advancing WMs.