In this talk, we consider porous medium type equations with the divergence form of drift that can be applied to fluid dynamics and math biology. The first part of the talk is about conditions on the drift concerning continuity of nonnegative weak solutions (joint work with K. Kang and Y. P. Zhang). The second part is about the existence of nonnegative weak solutions in the Wasserstein space where the nonlinear diffusion and initial data affect the scaling invariant classes of the drift (joint work with K. Kang and H. Kim).