The SQG equation models the formation of fronts of hot and cold air. In a different direction this system was proposed as a 2D model for the 3D incompressible Euler equations. It is not known at this moment if this equation can produce singularities. In this talk I will discuss some recent work on the existence of nontrivial families of global solutions of the SQG equation and related models. Joint work with Angel Castro, Diego Cordoba and Alex Ionescu.