The purpose of this study was to review the existing research on affect (beliefs, attitudes, and emotions) of elementary prospective teachers (EPTs) in university mathematics content courses. We use as our time period from publication in the United States of the Curriculum and Evaluation Standards for Schools Mathematics through 2016. A search of a combination of electronic databases and targeted international journals resulted in a total of 11 studies that looked at some aspect of affect with EPTs in all or some part of a university mathematics course over the 27-year time period. Nine of the 11 studies occurred in the context of a course or courses categorized as involving an alternative pedagogy that was student-centered. Overall we found that a student-centered approach to instruction supported changes in EPTs' affect that align with pedagogical recommendations in reform documents such as the NCTM Standards. However, shifts were sometimes difficult to come by and encountered resistance from EPTs. Implications for course learning experiences are offered and conflicting results between studies suggest directions for future research.