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The concept of chaotic advection was developed some twenty years ago as an outgrowth of work on advection by interacting point vortices. The term “chaotic advection” was first introduced in the title of an abstract for the 35th annual meeting of the American Physical Society (APS) Division of Fluid Dynamics (DFD) in 1982. The main reference, a Journal of Fluid Mechanics paper published in 1984, may be the true “birthdate” of the term. Earlier work from the 1960s by Arnol’d and Hénon on advection by steady three-dimensional flows already contained closely related ideas and results but was not widely appreciated. The present paper, based on the 2000 Otto Laporte Memorial Lecture delivered at the 53rd APS/DFD annual meeting, traces these and other precursors and the development of chaotic advection over the past two decades. Some exciting recent developments, such as application to fluid mixing in micro-electromechanical systems (MEMS) and to materials processing, and the introduction of topological methods of analysis, are highlighted. On balance, chaotic advection is now established as a subtopic of fluid mechanics with wide ramifications and continued promise for theory, experiment and applications.