After discussing the Hamiltonian structure of Chern-Simons theories, the standard procedure to study asymptotic symmetries in three-dimensional Chern-Simons gravity will be reviewed. Subsequently, we will turn our attention to the case of a Chern-Simons theory based on the Maxwell algebra. We will show that the boundary dynamics of this gravity theory is described by an enhancement of the bms_3 algebra with three independent central charges. This symmetry is characterized by the presence of Abelian generators, which modify the commutation relations of the super-translations in the standard bms_3 algebra. The result can be also obtained as an Inönü-Wigner contraction of three-copies of the Virasoro algebra, which in turn corresponds to the asymptotic symmetry of a Chern-Simons theory invariant under the AdS-Lorentz algebra. The realization of these new infinite-dimensional symmetries in the context of two-dimensional dual field theories will be discussed and possible generalizations of these results to the case of non-relativistic gravity theories and higher spin theories will be considered.