Each year, thousands of undergraduates in the science, technology, engineering, and mathematics (STEM) fields conduct research in US university and college laboratories. Such undergraduate research (UR) experiences are common practice in US higher education, with nearly a century of history at research universities and liberal arts colleges. Crucial in defining UR experiences is the apprenticeship of the novice researcher to an experienced scientist. A growing body of evidence indicates that apprentice-model undergraduate research does indeed offer many benefits to students in the short and longer term. Research experiences can powerfully shape students' knowledge, confidence, and readiness for careers and graduate education, whether in science or another field. These good outcomes for students are crafted by research advisors who supervise students' work and guide their development. Investigating an authentic scientific problem using real disciplinary tools motivates and gives intellectual significance to the investigation; it also offers a limitless supply of teachable moments that skilled advisors can exploit for their deep educational value. But doing "real science" also exposes a fundamental tension inherent to undergraduate research: Is it at heart an educational endeavor for students or a scholarly endeavor for faculty? In this article, the authors explore this fundamental tension between education and scholarship in undergraduate research and how it plays out for students, faculty, and institutions. (Contains 2 figures and 5 resources.)