Studies on two-phase flows are of interest in many fundamental problems and industrial applications, as the spray formation in internal combustion engine, the bubble formation in heat exchangers, the fluid management in satellites or space launcher tanks, the spray cooling or the interaction of bubbles with acoustic waves. The Direct Numerical Simulation is a powerful tool, which is complementary to experimental measurements, to provide accurate results in complex situations. However, unlike single-phase flows, currently the direct numerical simulation of two-phase flows cannot be considered as a fully mature field, especially in most configurations involving strong coupling between the interface motion with heat and mass transfer, acoustic or shock waves, and/or a solid boundary where a contact line can be formed. Nowadays, an important scientific community, at the frontier between fluid mechanics, heat and mass transfer and applied mathematics, is interested by the development of new numerical methods in order to improve the abilities, the accuracy and the stability of the Computational Multiphase Flows Dynamics algorithms. This presentation will emphasize on the development of new numerical methods to perform accurate Direct Numerical Simulations of two-phase flows. The interest of these numerical developments will be demonstrated on various applications, as shape oscillations of rising bubbles, Leidenfrost droplets, nucleate boiling, spray formation, free surface flow in a rotating spherical tank or the interaction of bubbles with ultrasound waves…