Abstract: Adaptive Cartesian grids play a crucial role in simulation fields due to their adaptiveness, orthogonality, and scalability. This paper first provides a comprehensive review of the theoretical foundation of adaptive Cartesian grids, including grid classification, GPU-based parallel grid construction algorithms, grid discretization schemes, and template design for differential operators. Then, from the perspectives of static models and dynamic simulations, it compares and analyzes the performance of different grid types in terms of spatial complexity and the time complexity of grid construction algorithms. Furthermore, this paper demonstrates the broad applicability and great potential of adaptive Cartesian grids in practical applications by constructing several examples, including shallow water wave simulation, Boolean operation-based solid modeling, and elastic collision simulations. Finally, the paper looks ahead to the future development directions of adaptive Cartesian grid technology, highlighting potential research paths and challenges.