The performance, field utility, and low cost of lateral flow assays (LFAs) have driven a tremendous shift in global health care practices by enabling diagnostic testing in previously unserved settings. This success has motivated the continued improvement of LFAs through increasingly sophisticated materials and reagents. However, our mechanistic understanding of the underlying processes that drive the informed design of these systems has not received commensurate attention. Here, we review the principles underpinning LFAs and the historical evolution of theory to predict their performance. As this theory is integrated into computational models and becomes testable, the criteria for quantifying performance and validating predictive power are critical. The integration of computational design with LFA development offers a promising and coherent framework to choose from an increasing number of novel materials, techniques, and reagents to deliver the low-cost, high-fidelity assays of the future.