This chapter is about the case for assigning taxing powers to subnational governments, and about the structure of this revenue assignment. As Musgrave (1983) put it in perhaps the seminal paper on this subject, ‘Who Should Tax, Where and What’? This review reconsiders the Musgrave questions after 25 years, asks whether the international trend in tax assignment is in step with what economists have prescribed, and concludes with some thoughts about the most likely future for the decentralization of tax systems. We begin with a discussion of the concept of revenue assignment, and with the theoretical justifications and a priori reasoning usually given for revenue assignment to subnational governments. A basic issue taken up in this discussion is whether the practice matches up with the theory. In the following section, we turn to a consideration of the case for decentralizing each of the major tax bases. Throughout this discussion, we distinguish among industrial, transition, and developing countries.