In both computer graphics and computational physics, fluid simulation techniques have traditionally expressed the geometry and topology of deforming liquid bodies using implicit representations, such as particles, level sets, or density fields. While these methods sidestep the handling of topological operations, such as merging and splitting, there is no free lunch: these methods can suffer from temporal incoherence issues, challenges in reconstructing a high-quality surface, substantial volume loss, or difficulties in treating thin and detailed features. I will give an overview of our recent work that instead represents the liquid surface geometry explicitly with dynamically adapting triangle meshes, and discuss how this general framework can be beneficially applied to animate dynamic splashing behavior, surface tension effects, very thin sheets of viscous liquid, and interactions among multiple immiscible liquids.