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Over the years, the Density Matrix Renormalization Group (DMRG) has established itself as the most powerful tool to study ground-state phase diagrams of strongly correlated one-dimensional systems. Access to excited states is in general significantly more involved. In my talk I will overview several approaches that have been developed to address this problem. In particular, I will show that exact excitation energies appear as locally site-independent modes if one records the excitation spectrum of the effective Hamiltonian while sweeping through the lattice in DMRG, a remarkable property since the effective Hamiltonian is only constructed to target the ground state. The results are spectacular for critical systems, for which the low-energy conformal tower of states can be obtained very accurately at essentially no additional cost.