Modeling of multiphase flow and reactive mass transport in porous media remains a pivotal challenge in the realm of subsurface energy storage, demanding a nuanced understanding across varying scales. This review paper presents a comprehensive overview of the latest advancements in multiscale modeling techniques that address the inherent complexity of these processes. Three cutting-edge approaches are presented: hybrid multiscale simulation, which leverages both continuum and discrete modeling frameworks to enhance model fidelity; approximated physics, which simplifies complex reactions and interactions to expedite computations without significantly sacrificing accuracy; and machine-learning-assisted multiscale simulation, which integrates predictive analytics to refine simulation outputs. Each method presents distinct advantages and hurdles, collectively advancing the precision and computational efficiency of subsurface modeling. Despite the substantial progress, we recognize the persistent challenges, such as the need for more robust coupling techniques, the balance between model complexity and computational feasibility, and effectively combining machine learning with traditional physical models. Promising directions for future work are discussed to address these challenges, aiming to push the boundaries of current multiscale modeling capabilities.