This book, the sixth in the series ``Collected Papers of John Milnor', contains all of Milnor's work on Real and Complex Dynamics from 1953 to 1999, plus one paper from 2000. These papers provide important and fundamental material in real and complex dynamical systems. Many of them have become classics in the field. Several questions addressed in them continue to be important in current research. Having them together in the same volume gives readers a taste of all the great mathematics developed by the author in the different areas of dynamics. In some cases, there have been minor corrections or clarifications, as well as references to more recent work which answers questions raised by the author. John Milnor's papers are accompanied by introductions that put them in perspective with respect to the current state of the field. There is also an index to facilitate searching the book for specific topics.