  Recently, there has been a wide interest in the study of aggregation
equations and Patlak-Keller-Segel (PKS) models for chemotaxis with degenerate
diffusion. The focus of this paper is the unification and generalization of the
well-posedness theory of these models. We prove local well-posedness on bounded
domains for dimensions $d\geq 2$ and in all of space for $d\geq 3$, the
uniqueness being a result previously not known for PKS with degenerate
diffusion. We generalize the notion of criticality for PKS and show that
subcritical problems are globally well-posed. For a fairly general class of
problems, we prove the existence of a critical mass which sharply divides the
possibility of finite time blow up and global existence. Moreover, we compute
the critical mass for fully general problems and show that solutions with
smaller mass exists globally. For a class of supercritical problems we prove
finite time blow up is possible for initial data of arbitrary mass.
