The continued growth in computing power, coupled with relatively recent advances in numerical methods, have made possible the study of a variety of multiphase flows at an unprecedented level of spatial-temporal detail. Two of these numerical methodologies will be presented in this talk, namely the Level Set and Volume-of-Fluid. While these methods have reached a certain degree of maturity, issues regarding numerical accuracy with respect to advection, dynamics, reinitialization, and spurious interface currents continue to draw attention and will be discussed. To illustrate the study of physics afforded by the exercise of these methodologies, two example problems will be presented. The first concerns primary atomization/droplet formation in liquid sprays. A key observation from this work is that the formation of droplets is preceded by the stretching of a liquid ligament. Hence, the effect of fuel properties on the final droplet formation can borrow from a numerical examination of the Rayleigh-Plateau instability. The second example problem consists of the impingement of multiple droplets on a heated surface. Results show that the boundary layer thickness is mostly affected by changes in inter-droplet spacing, Reynolds, and Peclet number, and influenced minimally by variations in Weber number and initial film thickness. In fact, it is explicitly demonstrated that the impact velocity has the greatest effect in local heat transfer. An analytical expression for the Nusselt number radial profile is also developed. It shows that the Nusselt number scales as ∼ Re 1/2, and its radial dependence is ∼ √r , which is the same as the circular jet impingement case. A notable departure from existing Nusselt number relationships is the presence of inter-droplet spacing, which plays a significant role in the multiple droplet configuration.