This study examined the contribution of perceptual and cognitive factors to speech-perception abilities in cochlear-implant (CI) users. Thirty CI users were tested on word intelligibility in sentences with and without semantic context, presented in quiet and in noise. Performance was compared with measures of spectral-ripple detection and discrimination, thought to reflect peripheral processing, as well as with cognitive measures of working memory and non-verbal intelligence. Thirty age-matched and thirty younger normal-hearing (NH) adults also participated, listening via tone-excited vocoders, adjusted to produce mean performance for speech in noise comparable to that of the CI group. Results suggest that CI users may rely more heavily on semantic context than younger or older NH listeners, and that non-auditory working memory explains significant variance in the CI and age-matched NH groups. Between-subject variability in spectral-ripple detection thresholds was similar across groups, despite the spectral resolution for all NH listeners being limited by the same vocoder, whereas speech perception scores were more variable between CI users than between NH listeners. The results highlight the potential importance of central factors in explaining individual differences in CI users and question the extent to which standard measures of spectral resolution in CIs reflect purely peripheral processing.