Mathematics education in the United States will be shaped at all levels by those who hold doctorates in the field. As professors, they influence the structure and content of university programs in mathematics education, where future teachers are prepared. As scholars, they engage in research and lead us to a deeper and better understanding of the field. This book is a detailed study of doctoral programs in mathematics education. It stems from a national conference sponsored by the National Science Foundation. It involved participants from across the United States, as well as Brazil, Japan, Norway, and Spain, and followed up the work of an earlier conference, published in One Field, Many Paths: U.S. Doctoral Programs in Mathematics Education (Volume 9 in this series). The book, as was the conference, is organized around several major questions, including: What is the core knowledge for doctoral students in mathematics education? What are the important issues and challenges in delivering doctoral programs? What can we learn about doctoral preparation by comparisons with other countries?What effect would accreditation of doctoral programs in mathematics education have on the profession?What next steps need to be addressed now? The book documents the wide range of ideas about doctoral programs in mathematics education and their varied features. It provides readers with current visions and issues concerning doctoral studies in the field and serves as a reminder that establishing stewards of the discipline of mathematics education is a continuing challenge.