Electronic resonances are metastable states with finite lifetime embedded in the ionization or detachment continuum. They are ubiquitous in chemistry, physics, and biology. Resonances play a central role in processes as diverse as DNA radiolysis, plasmonic catalysis, and attosecond spectroscopy. This review describes novel equation-of-motion coupled-cluster (EOM-CC) methods designed to treat resonances and bound states on an equal footing. Built on complex-variable techniques such as complex scaling and complex absorbing potentials that allow resonances to be associated with a single eigenstate of the molecular Hamiltonian rather than several continuum eigenstates, these methods extend electronic-structure tools developed for bound states to electronic resonances. Selected examples emphasize the formal advantages as well as the numerical accuracy of EOM-CC in the treatment of electronic resonances. Connections to experimental observables such as spectra and cross sections, as well as practical aspects of implementing complex-valued approaches, are also discussed.