In this introductory chapter, we summarize each of this volume's parts and the particular contributions that fall under them: I) the computability of physical systems and physical systems as computers, II) the implementation of computation in physical systems, III) physical perspectives on computer science, and IV) computational perspectives on physical theory. Before we do so, however, we review some of the basic concepts which will generally be taken for granted in the rest of the book, including those from: I) computability theory, Turing machines, and the Church-Turing thesis, II) computational complexity theory, III) quantum computing, IV) theories of computational implementation and the variety of “physical” Church-Turing theses, and V) Landauer's principle and the thermodynamics of computation.