The Core and the Periphery is a collection of papers inspired by the linguistics career of Ivan A. Sag (1949-2013), written to commemorate his many contributions to the field. Sag was professor of linguistics at Stanford University from 1979 to 2013; served as the director of the Symbolic Systems Program from 2005 to 2009; authored, co-authored, or edited fifteen volumes on linguistics; and was at the forefront of non-transformational approaches to syntax. Reflecting the breadth of Sag’s theoretical interests and approaches to linguistic problems, the papers collected here tackle a range of grammar-related issues using corpora, intuitions, and laboratory experiments. They are united by their use of and commitment to rich datasets and share the perspective that the best theories of grammar attempt to account for the full diversity and complexity of language data.