Pitch is a defining perceptual property of many real-world sounds, including music and speech. Classically, theories of pitch perception have differentiated between temporal and spectral cues. These cues are rendered distinct by the frequency resolution of the ear, such that some frequencies produce "resolved" peaks of excitation in the cochlea, whereas others are "unresolved," providing a pitch cue only via their temporal fluctuations. Despite longstanding interest, the neural structures that process pitch, and their relationship to these cues, have remained controversial. Here, using fMRI in humans, we report the following: (1) consistent with previous reports, all subjects exhibited pitch-sensitive cortical regions that responded substantially more to harmonic tones than frequency-matched noise; (2) the response of these regions was mainly driven by spectrally resolved harmonics, although they also exhibited a weak but consistent response to unresolved harmonics relative to noise; (3) the response of pitch-sensitive regions to a parametric manipulation of resolvability tracked psychophysical discrimination thresholds for the same stimuli; and (4) pitch-sensitive regions were localized to specific tonotopic regions of anterior auditory cortex, extending from a low-frequency region of primary auditory cortex into a more anterior and less frequency-selective region of nonprimary auditory cortex. These results demonstrate that cortical pitch responses are located in a stereotyped region of anterior auditory cortex and are predominantly driven by resolved frequency components in a way that mirrors behavior.