In this talk, I will introduce a free boundary problem arising in fluid mechanics called the Navier-Stokes problem with surface tension. After giving a brief history and overview of numerous versions of this problem, I will present my thesis results on the quasi-stationary approximation of the two-phase version of this problem, called the Stokes flow problem with surface tension. I will outline the structure of the proof, highlighting some of the key ideas that can be generalized to establish well-posedness of a certain class of interfacial fluid problems. I will compare and contrast the model I studied with the Muskat and Peskin problems.