In this talk we survey several new results for turbulent flows driven by a shear which is perpendicular to a stable stratification. First we show how in a body forced system layer formation can be associated to a stratified linear instability via nonlinear unstable steady solutions. We also show how mixing processes can be encapsulated by unstable periodic orbits embedded in the turbulence. Next we explore the differences when we instead drive the flow by moving boundaries in a plane Couette flow configuration. Here we find layers confined near the walls which are seemingly disconnected from any linear mechanism. However the layer scale provides insight into the way turbulence is shut-off when stratification becomes very large. Finally we investigate the effect of linear instabilities on the transition to turbulence in this system at very large Reynolds numbers and stratifications.