I will talk about various ``mixing'' questions that have attracted interest recently. For instance, ``Can you stir your coffee to keep it hot for longer'', or ``How well can you stir cream into your coffee, and at what cost?''.Mathematically these questions translate into studying a negative Sobolev norm of a passively advected scalar. The study of such questions also involves very interesting connection Bressan's (still open!) rearrangement cost conjecture. I will spend most of the talk surveying recent results, and conclude with brief description of joint work with A. Kiselev, Xiaoqian Xu and myself.