The 3D Quasi-Geostrophic system is a set of equations used in meteorology to describe the evolution of the atmosphere. The surface quasi-geostrophic equation (2D SQG) is a well-studied special case where the atmosphere above the earth is at rest. In this talk, we will discuss some recent results.  The first two derive boundary conditions for the 3D QG posed in a cylinder and construct global in time weak solutions and local-in-time classical solutions. The second result shows the non-uniqueness of weak solutions to the 3D model via a convex integration argument.