The analysis and control of mixing is of great interest because of the potential for optimizing the performance of many flow processes. This monograph presents a unique overview of the physics, mathematics and state-of-the-art theoretical/numerical modeling and experimental investigations of mixing. It approaches the subject of mixing from many angles: presents theoretical and experimental results, discusses laminar and turbulent flows, considers macro and micro scales, elaborates on purely advective and advective-diffusive flows, and considers conceptual and industrial-relevant mixing devices. This monograph provides an essential reading for graduate students and postdoctoral researches interested in the investigation of mixing, and constitutes an indispensable reference for mechanical, chemical and aeronautical engineers, and applied mathematicians in universities and industries.