In this talk, we will discuss the initial value problem for 3D interfacial fluid flows with surface tension. We will emphasize the case in which the fluid velocities are given by Darcy's Law; this can serve as a model for intefacial flow in a porous medium.  We will discuss a well-posedness proof for the problem, with the initial data in Sobolev spaces.  We will also discuss a non-stiff numerical method; this is similar in spirit to the method of Hou, Lowengrub, and Shelley for the corresponding 2D problem. Finally, we will give some of the details of a convergence proof for a variant of this numerical method; this convergence proof requires estimates which are similar in spirit to the estimates required to demonstrate well-posedness.  The results discussed may include joint work with Nader Masmoudi, Michael Siegel, Svetlana Tlupova, and Yang Liu.