This article raises the question of what K–12 teachers need to know to teach mathematics and science well. It begins by examining reform proposals for K–12 science and mathematics teaching with an eye toward defining what good teaching practice consists of. It then examines a wide range of literature to delineate the varieties of knowledge that have been associated with this kind of teaching. While the focus is on subject matter knowledge, the article addressed the character of that knowledge rather than the content of that knowledge. Types of knowledge identified in the literature include conceptual understanding of the subject, pedagogical content knowledge, beliefs about the nature of work in science and mathematics, attitudes toward these subjects, and actual teaching practices with students. The literature is incomplete with respect to which of these is relatively more or relatively less important. © 1998 John Wiley & Sons, Inc. J Res Sci Teach 35: 249–263, 1998.