We will explain what derived manifolds and derived differential geometry are, and how they naturally arise from the viewpoint of Feynman’s path-integration. We will then explain a rigorous construction of the ”derived space of solutions” to the field equations of a Lagrangian gauge field theory, and how this naturally gives rise to a notion of globalized BV-quantization. Much of this is joint work with Owen Gwilliam. No familiarity with any of the terms mentioned in this abstract will be assumed.