Grid-centric perception is a crucial field for mobile robot perception and navigation. Nonetheless, grid-centric perception is less prevalent than object-centric perception as autonomous vehicles need to accurately perceive highly dynamic, large-scale traffic scenarios and the complexity and computational costs of grid-centric perception are high. In recent years, the rapid development of deep learning techniques and hardware provides fresh insights into the evolution of grid-centric perception. The fundamental difference between grid-centric and object-centric pipeline lies in that grid-centric perception follows a geometry-first paradigm which is more robust to the open-world driving scenarios with endless long-tailed semantically-unknown obstacles. Recent researches demonstrate the great advantages of grid-centric perception, such as comprehensive fine-grained environmental representation, greater robustness to occlusion and irregular shaped objects, better ground estimation, and safer planning policies. There is also a growing trend that the capacity of occupancy networks are greatly expanded to 4D scene perception and prediction and latest techniques are highly related to new research topics such as 4D occupancy forecasting, generative AI and world models in the field of autonomous driving. Given the lack of current surveys for this rapidly expanding field, we present a hierarchically-structured review of grid-centric perception for autonomous vehicles. We organize previous and current knowledge of occupancy grid techniques along the main vein from 2D BEV grids to 3D occupancy to 4D occupancy forecasting. We additionally summarize label-efficient occupancy learning and the role of grid-centric perception in driving systems. Lastly, we present a summary of the current research trend and provide future outlooks.