Tensor network states (TNSs) have independently advanced the fields of condensed matter physics, electronic structure theory, and vibrational quantum dynamics. Despite their similarities, TNS algorithms applied to electronic and vibrational systems differ substantially. In this talk, I will explore the application of the density matrix renormalization group (DMRG) - traditionally used for condensed matter and electronic structure simulations - to vibrational quantum dynamics. I will compare the performance of the DMRG with the multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) method, an established algorithm for vibrational systems. I will use these methods to simulate the vibrational spectra of the Zundel ion (H$_{5}$O$_{2}$$^{+}$) and the 33-dimensional Eigen ion, two highly challenging systems characterized by large-amplitude motion and Fermi resonances. Finally, I will show how the DMRG can be used to simulate correlated real-time electron dynamics. These simulations reveal how, after ionization, an electronic hole, i.e., the positive, localized charge, rapidly migrates in a molecule. I will how this is affected by electronic orbital interactions.