With the launch of NASA's Kepler mission, stellar astrophysics in general, and the eclipsing binary star field in particular, has witnessed a surge in data quality, interpretation possibilities, and the ability to confront theoretical predictions with observations. The unprecedented data accuracy and an essentially uninterrupted observing mode of over 2000 eclipsing binaries is revolutionizing the field. Amidst all this excitement, we came to realize that our best models to describe the physical and geometric properties of binaries are not good enough. Systematic errors are evident in a large range of binary light curves, and the residuals are anything but Gaussian. This is crucial because it limits us in the precision of the attained parameters. Since eclipsing binary stars are prime targets for determining the fundamental properties of stars, including their ages and distances, the penalty for this loss of accuracy affects other areas of astrophysics as well. Here, we propose to substantially revamp our current models by applying the lessons learned while reducing, modeling, and analyzing Kepler data.