ABSTRACT
In this chapter, we examine the modeling issues arising in the mathematical description of disintegration of liquid volumes. The two representative examples to be considered from this general class are the breakup of axisymmetric liquid threads and the rupture of films. Singular solutions obtained in the framework of the standard model and a regular way of describing the breakup phenomenon are discussed and compared with experimental observations. We conclude by giving a brief overview of the modeling difficulties emerging when one applies the continuum approach on mesoscopic length scales and some results obtained on this way.