Dense astrophysical environments can host black hole binaries whose orbits are not fully circularized by the time of the merger. The gravitational waves generated by these systems bear distinct signatures of the binary dynamics, significantly deviating from the waveforms emitted by circularized black hole binaries. The understanding of these eccentric binaries is thus fundamental for the scientific goals of the LIGO-Virgo-KAGRA collaboration and future third-generation gravitational wave detectors. In this seminar, we provide an overview on how effective-one-body models and numerical relativity simulations can be utilized to describe the dynamics and the waveforms of these systems, addressing both bound and unbound dynamics.