Droplets, bubbles and interfaces offer fascinating physical and mathematical problems
and are a key part of the microscopic modeling of multiphase flow in porous media and other
contexts. The talk will describe how to address these problems numerically, using tools such as the
Volume of Fluid method. In particular, I will discuss the problems of contact line motion,
the invasion of porous media and turbulent free-surface flows. The issues arising from
the upscaling of simulations to more extreme HPC environments
will also be discussed.