The notion of controversy space is the key element of the new model of philosophical and scientific change introduced in this book. Devised as an alternative to classical models, the model of Controversy Spaces is a heuristic tool for the reconstruction of processes of conceptual change in the history of science and philosophy. The first chapter of this volume outlines in its initial section the historical trajectory of the dialectical, adversarial approach to the progress of knowledge, from its ancient flourishing and its almost complete oblivion in modernity up to its contemporary revival. Then the main features that characterize the structure and dynamics of controversy spaces are identified and examined. In the rest of the book the reader will find a detailed, fascinating series of case studies that apply the CS model in a variety of scientific areas, ranging from physics to linguistics, as well as the philosophy of mind and the philosophy of historiography.