This is an announcement of a description of loop Grassmannians of reductive groups in the setting of “local spaces” over a curve. The structure of a local space is a version of the fundamental structure of a factorisable space introduced and studied by Beilinson and Drinfeld. The weakening of the requirements formalizes some well known examples of “almost factorisable spaces'' and constructions with such spaces Much of the material comes from a joint work with Kamnitzer and Knutson.