The birth of the theory of chaotic advection is usually traced back to a 1984 paper
by Hassan Aref. In this work, Aref studied the mixing induced by two vortices switched alternately on and off inside an inviscid fluid. This seminal work had been made possible by earlier developments in the fields of dynamical Systems and fluid mechanics in the previous decades. Vladimir Arnold
and Michel Hénon
had already noticed that the trajectories advected by area-preserving three-dimensional flows could be chaotic. However, the practical interest of chaotic advection for fluid mixing applications remained unnoticed until the work of Aref in the 80's. Since then, the whole toolkit of dynamical systems and chaos theory has been used to characterize fluid mixing by chaotic advection. Recent work has for example employed topological methods to characterize the stretching of fluid particles. Other recent directions of research concern the study of chaotic advection in complex flows, such as granular flows.