This article explores the concept of black boxes within mathematical modeling. First, we perform a literature-based clarification of the term black box, the use of a black box, and explore the use of this construct in science, and workplace. A black box is characterized by the following issues: (a) being believed to be distinct, (b) having observable (and relatable) inputs and outputs, (c) being black (that is, opaque to the observer). Afterwards, we demonstrate the uses of black boxes within mathematical modeling. We generalize these uses to a model of how black boxes can be implemented in mathematics education. Based on this model, we derive educationally relevant activities for using and opening such a black box. The application of these activities is illustrated in more details using an example of physical chemistry: the Arrhenius Equation.