This article presents a review of literature exploring five different perspectives on mathematical modeling in mathematics education. Because there is not a single agreed-on definition of what mathematical modeling is or how it should be done, a focused and extensive review of mathematical modeling is essential. The five broad classifications discussed in this article include realistic modeling, educational modeling, models and modeling perspective, socio-critical modeling, and epistemological modeling. For each perspective, we present (a) the goals of mathematical modeling, (b) the definition of a mathematical model, (c) the mathematical modeling cycle, (d) the design of the modeling task, and (e) key researchers and research foci. In this article, we aim to present the different perspectives of mathematical modeling in an organized way so as to (1) demonstrate the rich and diverse background of mathematical modeling and (2) clarify theoretical foundations of seminal works in mathematical modeling.