Mixed hp-FEM for incompressible fluid flow on anisotropic meshes are analyzed. A discrete inf-sup condition is proved with a constant independent of the meshwidth and the aspect ratio. For each polynomial degree $k\geq 2$, velocity-pressure subspace pairs are presented which are stable on quadrilateral mesh-patches, independently of the element aspect ratio implying in particular divergence stability on the so-called Shishkin-meshes. ...