The KPZ equation is a conjecturally universal model for many dynamical interface fluctuations, introduced by Kardar, Parisi, and Zhang. The main result of this talk is a rigorous derivation of the KPZ equation as a scaling limit for a class of Ginzburg-Landau SPDEs, which itself is a large part of the motivation in Kardar, Parisi, and Zhang's original paper. This also gives the first derivation of random matrix statistics from this general class of Ginzburg-Landau SPDEs