Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes undergraduate students to mathematics as it can be applied to real-world problem-solving. We give an outline of the rules, structure, and outcomes from the contest, including student feedback and a discussion of the different levels of modeling that we have seen from students in the 6-year span of the contest. Finally, we offer suggestions on how to prepare students for the Challenge, and describe the process for participating.