Complex-analytic methods have revolutionized the study of low-dimensional dynamics during the last several decades. A beautiful synthesis of techniques has emerged, creating a new field which has combined such seemingly disjoint topics such as the structure of the Mandelbrot set, the stochastic properties of a typical interval map, Feigenbaum-Coullet-Tresser universality and renormalization, among many others. Misha Lyubich’s work has been central to the development of this field, and his 60th birthday gives us an opportunity to take stock of the current state of the art, as well as to chart new directions. The aim of the conference is to bring together experts working in the area of complex and real low-dimensional dynamics, and closely related fields of conformal geometry, groups and foliations and general smooth dynamical systems. This wide range of topics is tied together by the general theme of the use of complex methods in dynamics.