The masses of fermions and gauge bosons enter the Standard Model through the Higgs mechanism, which is satisfactory technically but is not understood physically. We do not know what nature really does to give mass to particles, nor what experimental clues will lead us to nature's solution. Understanding Higgs physics is necessary in order to complete the Standard Model, and to learn how to extend it and improve its foundations.This book is a collection of current work and thinking about these questions by active workers. It speculates about what form the answers will take, as well as updates and extends previous books and reviews. Some chapters emphasize theoretical questions, some focus on connections with other areas of physics, and some discuss how we can get the data to uncover nature's solution.