Multiphase flows are central to many manufacturing and processing technologies, with applications spanning energy generation, material science and biomedical settings. Despite advancing computational resources, the complex dynamics of production processes are challenging to simulate, and the use of empirical correlations remains the norm. This talk will summarise recent efforts to develop predictive numerical tools that can be used as a basis for engineering design. In a multi-fidelity approach, we apply highly resolved hybrid front-tracking techniques to clarify fundamental flow features, and utilise low-cost simulation variants to address engineering design questions. We will share simulation results inspired by industrially relevant problems related to liquid–liquid displacements in pipe flows, mixing of miscible and immiscible fluids, two-phase flows with and without surfactants, and two- and three-phase microfluidics, amongst others. The simulation techniques presented can be coupled to novel surrogate models for exploiting advances in optimisation and machine learning, being the new frontier in multiphase fluid dynamics.