This brief introductory chapter begins with the key question to be addressed in the book: why does brain size vary among animal species? It contains a short outline of the book’s contents and establishes the rationale for the examination of the evidence that has been gathered using the comparative method over the past five decades. I explain that the book will be both a review and a critique of the work that has attempted to explain which natural selection pressures led to changes in brain size. This is a focus that, to a large extent, excludes work that addresses mechanistic explanations for brain size.