Monaural spectral features are important for human sound-source localization in sagittal planes, including front-back discrimination and elevation perception. These directional features result from the acoustic filtering of incoming sounds by the listener's morphology and are described by listener-specific head-related transfer functions (HRTFs). This article proposes a probabilistic, functional model of sagittal-plane localization that is based on human listeners' HRTFs. The model approximates spectral auditory processing, accounts for acoustic and non-acoustic listener specificity, allows for predictions beyond the median plane, and directly predicts psychoacoustic measures of localization performance. The predictive power of the listener-specific modeling approach was verified under various experimental conditions: The model predicted effects on localization performance of band limitation, spectral warping, non-individualized HRTFs, spectral resolution, spectral ripples, and high-frequency attenuation in speech. The functionalities of vital model components were evaluated and discussed in detail. Positive spectral gradient extraction, sensorimotor mapping, and binaural weighting of monaural spatial information were addressed in particular. Potential applications of the model include predictions of psychophysical effects, for instance, in the context of virtual acoustics or hearing assistive devices.