The Hessian family of K3 surfaces has been studied for many years, with much of its geometry and moduli theory developed in foundational work by Dolgachev and Keum, Dardanelli and van Geemen, Koike, and Kondō. More recently, this four-parameter family has attracted renewed interest from the physics community through its appearance in the three-loop sunset Feynman integral. I will describe a modular parametrization of the family in terms of explicit Borcherds products, giving a direct interpretation of the three-loop Feynman integral in terms of automorphic forms. I will also indicate a connection between these Borcherds products and natural higher Chow cycles on Hessian K3 surfaces. This talk is based on ongoing joint work with C. Doran, E. Pichon-Pharabod, and P. Vanhove.