In recent years, the work of Guaraco, Hutchinson, Tonegawa, and Wickramasekera has established a min-max construction of minimal hypersurfaces in closed Riemannian manifolds, based on the analysis of singular limits of sequences of solutions of the Allen-Cahn equation, a semi-linear elliptic equation arising in the theory of phase transitions. In this talk, I will describe some recent boundary regularity results for such limit-interfaces, which provide the first step towards an Allen-Cahn min-max construction of free boundary minimal hypersurfaces in Riemannian manifolds with boundary. This is based on joint work with Martin Li (CUHK) and Davide Parise (UCSD).