Recent advancements in AI-generated content have significantly improved the realism of 3D and 4D generation. However, most existing methods prioritize appearance consistency while neglecting underlying physical principles, leading to artifacts such as unrealistic deformations, unstable dynamics, and implausible objects interactions. Incorporating physics priors into generative models has become a crucial research direction to enhance structural integrity and motion realism. This survey provides a review of physics-aware generative methods, systematically analyzing how physical constraints are integrated into 3D and 4D generation. First, we examine recent works in incorporating physical priors into static and dynamic 3D generation, categorizing methods based on representation types, including vision-based, NeRF-based, and Gaussian Splatting-based approaches. Second, we explore emerging techniques in 4D generation, focusing on methods that model temporal dynamics with physical simulations. Finally, we conduct a comparative analysis of major methods, highlighting their strengths, limitations, and suitability for different materials and motion dynamics. By presenting an in-depth analysis of physics-grounded AIGC, this survey aims to bridge the gap between generative models and physical realism, providing insights that inspire future research in physically consistent content generation.