As parameters in quantum mechanics are slowly varied, states undergo a non-Abelian holonomy known as Berry phase. I will review the ideas behind the Berry phase and explain how supersymmetry imposes restrictions on the holonomy. The associated non-Abelian gauge connections must obey certain first order equations which are related to the self-dual Yang-Mills equations, specifically the Hitchin equations, tt star equations, and Bogomolnyi equations. I will end by showing how one can build a BPS 't Hooft-Polyakov monopole in the lab.