abstract: Research on mixing in fluids splits into categories that – on the practical side - pertain to design and analysis of mixing protocols and control of mixing. I will review some of the mathematical concepts – specifically mix norms and mesohyperbolicity - useful in both problems with a specific attention to finite-time aspects. I will discuss how the concept of mesohyperbolicity enables extension of theories developed for laminar mixing to the realm of turbulent mixing. I will also discuss recent results on mixing and transport in high Reynolds number flows using these concepts.