Consider a three-dimensional closed container that contains an incompressible fluid, say water. Introduce ink at some location inside the container. Roughly speaking, mixing of ink and water will be better if fluid particle trajectories are more complicated. Fluid particle trajectories are governed by a three-dimensional system of time dependent volume-preserving ordinary differential equations. This puts the subject of fluid mixing within the context of dynamical systems and control theory of volume-preserving systems. In this talk I will present some elements of the theory of analysis and control of mixing. It is, in fact, the theory of measure-preserving systems with specific objectives, typically coming from ergodic theoretic considerations. The mixing objectives such as partition and Kolmogorov-Sinai entropy will be considered, a simple prototypical example of optimal control solved and applied in the context of a recent experiment. Another possible objective is maximization of flux between different regions of fluid domain. A prototypical example in which this objective is used will be presented. It involves reduced-order modeling using vortex elements. Ergodic theory concepts are also useful in visualization: I will present an idea for visualization of non-mixed regions in laminar flows. Experimental visualization results based on this analysis obtained by Sotiropoulos (Georgia Tech) and collaborators will be presented. Finally, the above analysis will be tested on design of a micromixer - a promising area for application of these dynamical systems-based ideas. I will argue that an actively-controlled design has advantages for mixing in microchannels over the competing strategies.