The mammalian cochlea is a complex organ of hearing that processes environmental sounds through mechanical and biophysical processes. The cochlea consists of three adjacent membranous tubes coiled in the form of a snail, enclosed by a bony shell. Environmental sounds are transmitted to the cochlea via the middle ear ossicles, causing vibrations in the basilar membrane (BM), which is the primary site of sound transduction. These vibrations travel along the BM, with their amplitude growing and then decaying, reaching a maximum at the characteristic frequency (CF) of each site. The location of this maximum is determined by the stimulus frequency, with high-frequency waves localized near the base and low-frequency waves near the apex of the cochlea. At the base of the cochlea, BM vibrations exhibit a compressive nonlinearity, where responses to stimuli near CF are sensitive and sharply frequency-tuned, while responses to intense stimuli are insensitive and poorly tuned. This nonlinearity is highly labile, indicating the presence of a positive feedback mechanism, the "cochlear amplifier," involving outer hair cells and their transduction currents. At the apex, nonlinearities are less prominent, suggesting a lesser role for the cochlear amplifier in determining mechanical responses to sound. The review discusses the mechanical processes leading to the stimulation of inner hair cells, including the vibrations of the BM, the organ of Corti, and the tectorial membrane (TM). It covers the anatomical and functional setting of the cochlea, historical highlights, and detailed analyses of BM mechanics at both the base and apex of the cochlea. The review also explores the properties of cochlear vibrations as a function of longitudinal position, the mapping of CF upon cochlear location, and the differences in response magnitudes and phases between the base and apex of the cochlea. Finally, it discusses the concept of cochlear traveling waves, including fast and slow waves, and their significance in the cochlear processing of sound.The mammalian cochlea is a complex organ of hearing that processes environmental sounds through mechanical and biophysical processes. The cochlea consists of three adjacent membranous tubes coiled in the form of a snail, enclosed by a bony shell. Environmental sounds are transmitted to the cochlea via the middle ear ossicles, causing vibrations in the basilar membrane (BM), which is the primary site of sound transduction. These vibrations travel along the BM, with their amplitude growing and then decaying, reaching a maximum at the characteristic frequency (CF) of each site. The location of this maximum is determined by the stimulus frequency, with high-frequency waves localized near the base and low-frequency waves near the apex of the cochlea. At the base of the cochlea, BM vibrations exhibit a compressive nonlinearity, where responses to stimuli near CF are sensitive and sharply frequency-tuned, while responses to intense stimuli are insensitive and poorly tuned. This nonlinearity is highly labile, indicating the presence of a positive feedback mechanism, the "cochlear amplifier," involving outer hair cells and their transduction currents. At the apex, nonlinearities are less prominent, suggesting a lesser role for the cochlear amplifier in determining mechanical responses to sound. The review discusses the mechanical processes leading to the stimulation of inner hair cells, including the vibrations of the BM, the organ of Corti, and the tectorial membrane (TM). It covers the anatomical and functional setting of the cochlea, historical highlights, and detailed analyses of BM mechanics at both the base and apex of the cochlea. The review also explores the properties of cochlear vibrations as a function of longitudinal position, the mapping of CF upon cochlear location, and the differences in response magnitudes and phases between the base and apex of the cochlea. Finally, it discusses the concept of cochlear traveling waves, including fast and slow waves, and their significance in the cochlear processing of sound.