Disabling hearing loss is the most common sensorineural disability worldwide. It affects around 466 million people and its incidence is expected to rise to around 900 million people by 2050, according to World Health Organization estimates. Most cases of hearing impairment are due to the degeneration of hair cells (HCs) in the cochlea, mechano-receptors that transduce incoming sound information into electrical signals that are sent to the brain. Damage to these cells is mainly caused by exposure to aminoglycoside antibiotics and to some anti-cancer drugs such as cisplatin, loud sounds, age, infections and genetic mutations. Hearing deficits may also result from damage to the spiral ganglion neurons that innervate cochlear HCs. Differently from what is observed in avian and non-mammalian species, there is no regeneration of missing sensory cell types in the adult mammalian cochlea, what makes hearing loss an irreversible process. This review summarizes the research that has been conducted with the aim of developing cell-based strategies that lead to sensory cell replacement in the adult cochlea and, ultimately, to hearing restoration. Two main lines of research are discussed, one directed toward the transplantation of exogenous replacement cells into the damaged tissue, and another that aims at reactivating the regenerative potential of putative progenitor cells in the adult inner ear. Results from some of the studies that have been conducted are presented and the advantages and drawbacks of the various approaches discussed.