Multiphase flow solvers in the engineering industry are dominated by models based on the volume of fluid or the level set approach. However, current capabilities fall short in several ways and our ability to make predictions is still very limited in problems involving phase transformations. Over the past decade, there has been significant progress in multiphase flow modeling and simulation driven by new theoretical and computational advances. The theoretical developments occurred in the area of phase-field modeling and have led to multiphase flow theories that, I contend, are superior to classical models (e.g., volume of fluid, level set or front tracking) in several aspects including: a more fundamental approach to represent phase transformations, a more accurate description of contact line dynamics, and a fully differentiable framework that allows straightforward integration with artificial intelligence algorithms. The computational developments emerged from new stabilization approaches and have been fueled by Isogeometric Analysis, which offers new possibilities for the discretization of the higher-order operators present in phase-field theories of multiphase flows. This talk will exemplify the possibilities of phase-field models of multiphase flows using two canonical examples. I will first discuss the Navier-Stokes-Cahn-Hilliard equations, a two-fluid model without phase transformations, in the context of contact line problems. I will then discuss Direct van der Waals simulation (DVS), a new computational paradigm to study liquid-vapor phase transformations that considers the non-equilibrium thermodynamics at liquid-vapor interfaces and does not rely on any phenomenological model for phase transformation. I will close the talk by showing new opportunities in multiphase flow modeling opened by Isogeometric Analysis and phase-field modeling.