During hearing, acoustic signals travel up the ascending auditory pathway from the cochlea to auditory cortex; efferent connections provide descending feedback. In human listeners, although auditory and cognitive processing have sometimes been viewed as separate domains, a growing body of work suggests they are intimately coupled. Here, we review the effects of hearing loss on neural systems supporting spoken language comprehension, beginning with age-related physiological decline. We suggest that listeners recruit domain general executive systems to maintain successful communication when the auditory signal is degraded, but that this compensatory processing has behavioral consequences: even relatively mild levels of hearing loss can lead to cascading cognitive effects that impact perception, comprehension, and memory, leading to increased listening effort during speech comprehension.