In general relativity (and other field theories with diffeomorphism symmetries) Noether's theorem does not give rise to a hamiltonian momentum map. This long-standing fundamental problem has a solution in the setting of multisymplectic geometry, where the map from spacetime vector fields to their Noether currents extends naturally to a morphism of L-infinity algebras, i.e. to a homotopy momentum map. I will report on the development of the notion of homotopy reduction, in particular on the definition of the homotopy zero locus and its natural diffeological structure. This is joint work with Janina Bernardy.