Using multiple representations (MR) such as graphs, symbols, diagrams, and text, is central to teaching and learning in physics classrooms. While different studies have provided evidence of the positive impact of the use of MR on physics learning, a comprehensive overview of existing literature on the use of MR in physics education, especially at the undergraduate level, is missing. This manuscript addresses this gap in the literature by reporting on the outcomes of a systematic review study that aimed to provide an overview of the existing knowledge base, to identify gaps in the knowledge base, and to propose future research about the use of MR in the context of undergraduate physics education. For the purpose of this study, we reviewed 24 empirical studies published between 2002 and 2019 in scientific, peer-reviewed journals in the context of undergraduate physics education. The outcomes of this review study are discussed under these themes (a) In what ways does the use of MR in instruction support student learning? (b) What kinds of representations do students use? (c) What difficulties do students face in using MR? (d) What is the relation between students' use of MR and students' problem-solving skills? and, (e) What is the added value of technology integration in teaching with MR? We identify gaps in the existing knowledge base, and we propose future research directions in these three areas: (a) Exploring the use of MR in university physics textbooks; (b) Blending of different kinds of MR; and, (c) The use of virtual reality applications.