Multiphase gas-ranging from cold molecular clouds ( \(\lesssim 100\,\) K) to hot, diffuse plasma ( \(\gtrsim 10^6\,\) K) is a defining feature of the interstellar, circumgalactic, intracluster, and intergalactic media. Accurately simulating its dynamics is critical to improving our understanding of galaxy formation and evolution, however, due to their multi-scale and multi-physics nature, multiphase systems are highly challenging to model. In this review, we provide a comprehensive overview of numerical simulations of multiphase gas in and around galaxies. We begin by outlining the environments where multiphase gas arises and the physical and computational challenges associated with its modeling. Key quantities that characterize multiphase gas dynamics are discussed, followed by an in-depth look at idealized setups such as turbulent mixing layers, cloud-wind interactions, thermal instability, and turbulent boxes. The review then transitions to less idealized and/or larger-scale simulations, covering radiative supernovae bubbles, tall box simulations, isolated galaxy models including dwarf and Milky Way-mass systems, and cosmological zoom-in simulations, with a particular focus on simulations that enhance resolution in the halo. Throughout, we emphasize the importance of connecting scales, extracting robust diagnostics, and comparing simulations to observations. We conclude by outlining persistent challenges and promising directions for future work in simulating the multiphase Universe.
