This paper explores significant advancements in the numerical simulation of multiphase, multi-physics flows within underground reservoirs, driven by the necessity to understand and manage complex geological and engineered systems. It delves into the latest research in numerical simulation techniques at both the pore and Darcy scales, emphasizing the integration of traditional methods with emerging machine learning technologies. Key simulation methods reviewed at the pore scale include the lattice Boltzmann method, level set method, phase field method, and volume of fluid method, each offering unique advantages and facing limitations related to computational efficiency and stability. Special attention is given to spontaneous imbibition, where capillary action facilitates the movement of wetting fluids into porous media. Discussions at the Darcy scale focus on macroscopic simulation methods that simplify microscale interactions but face challenges in accurately modeling the multiscale and heterogeneous nature of fractured media. Furthermore, an overview of the basic principles, limitations, and potential of integrating machine learning algorithms with traditional numerical methods emphasizes their role in enhancing simulation efficiency and stability. Future research will aim to address existing challenges and maximize the use of advanced computational technologies to refine the accuracy, efficiency, and practical applicability of multiphase and multifield flow simulations in underground reservoirs.