This paper is an invited perspective written in association with the awarding of the 2018 American Society of Mechanical Engineers Van C. Mow Medal. Inspired by Professor Mow's collaboration with Professor Michael Lai and the role mathematical modeling played in their work on cartilage biomechanics, this article uses our group's work on myocardial infarct healing as an example of the potential value of models in modern experimental biomechanics. Focusing more on the thought process and lessons learned from our studies on infarct mechanics than on the details of the science, this article argues that the complexity of current research questions and the wealth of information already available about almost any cell, tissue, or organ should change how we approach problems and design experiments. In particular, this paper proposes that constructing a mathematical or computational model is now in many cases a critical prerequisite to designing scientifically useful, informative experiments.