The rapid progress in embodied artificial intelligence has highlighted the necessity for more advanced and integrated models that can perceive, interpret, and predict environmental dynamics. In this context, World Models (WMs) have been introduced to provide embodied agents with the abilities to anticipate future environmental states and fill in knowledge gaps, thereby enhancing agents' ability to plan and execute actions. However, when dealing with embodied agents it is fundamental to ensure that predictions are safe for both the agent and the environment. In this article, we conduct a comprehensive literature review of World Models in the domains of autonomous driving and robotics, with a specific focus on the safety implications of scene and control generation tasks. Our review is complemented by an empirical analysis, wherein we collect and examine predictions from state-of-the-art models, identify and categorize common faults (herein referred to as pathologies), and provide a quantitative evaluation of the results.