Speech is characterized by temporal and spectral modulations. Hearing-impaired (HI) listeners may have reduced spectrotemporal modulation (STM) sensitivity, which could affect their speech understanding. This study examined effects of hearing loss and absolute frequency on STM sensitivity and their relationship to speech intelligibility, frequency selectivity and temporal fine-structure (TFS) sensitivity. Sensitivity to STM applied to four-octave or one-octave noise carriers were measured for normal-hearing and HI listeners as a function of spectral modulation, temporal modulation and absolute frequency. Across-frequency variation in STM sensitivity suggests that broadband measurements do not sufficiently characterize performance. Results were simulated with a cortical STM-sensitivity model. No correlation was found between the reduced frequency selectivity required in the model to explain the HI STM data and more direct notched-noise estimates. Correlations between low-frequency and broadband STM performance, speech intelligibility and frequency-modulation sensitivity suggest that speech and STM processing may depend on the ability to use TFS.