We study the large gauge transformations of massless fields with arbitrary integer spin, in any spacetime dimension. Upon imposing radiation-like falloff conditions, analogous to the asymptotic flatness conditions for gravitational systems, we calculate the associated asymptotic surface charges, the energy flux and, in the Yang-Mills case, the charge flux at null infinity. In four di- mensions, this approach identifies an infinite-dimensional family of higher-spin asymptotic symmetries, whose Ward identities yield Weinberg’s soft theorem. Infinite-dimensional asymptotic symmetries in higher dimensions require instead a less restrictive choice of falloffs, which we illustrate in the case of spin one with emphasis on the definition of the corresponding surface charges and on the cal- culation of memory effects.