What is mixing and can it be complex?

While the concept of mixing is commonly used in science and engineering, its exact interpretation may vary between different disciplines. In the present work, we analyse the concept of mixing in context of mechanical mixing, the ergodic theory, modelling of turbulent reacting fluid flows and complex competitive systems. Although mixing represents a dissipative process, which is responsible for irreversible increase of molecular disorder, mixing nevertheless can be associated with emergence of complexity under certain conditions. This dual role of mixing is noted and examined here. The appendix discusses three fundamental hypotheses, which are related to understanding of mixing and were introduced by Boltzmann. (paper)