Abstract: Realistic animation of various interactions between multiple fluids, possibly undergoing phase change, is a challenging task in computer graphics. The visual scope of multi-phase multi-fluid phenomena covers complex tangled surface structures and rich color variations, which can greatly enhance visual effect in graphics applications. Describing such phenomena requires more complex models to handle challenges involving calculation of interactions, dynamics and spatial distribution of multiple phases, which are often involved and hard to obtain real-time performance. Recently, a diverse set of algorithms have been introduced to implement the complex multi-fluid phenomena based on the governing physical laws and novel discretization methods to accelerate the overall computation while ensuring numerical stability. By sorting through the target phenomena of recent research in the broad subject of multiple fluid, this state-of-the-art report summarizes recent advances on multi-fluid simulation in computer graphics.