We discuss regularity questions for fluid models motivated by the Navier-Stokes and Euler equations. We begin by analyzing the toy-example of the fractal Burgers equation, and then focus on the surface quasi-geostrophic (SQG) equation. The main tool presented here is a new nonlinear maximum principle for equations with drift and dissipation. As an application we give the proof of global regularity for the critical SQG equation.