Purpose: The goal of this study was to determine how background noise, linguistic properties of spoken sentences, and listener abilities (hearing sensitivity and verbal working memory) affect cognitive demand during auditory sentence comprehension. Method: We tested 30 young adults and 30 older adults. Participants heard lists of sentences in quiet and in 8-talker babble at signal-to-noise ratios of +15 dB and +5 dB, which increased acoustic challenge but left the speech largely intelligible. Half of the sentences contained semantically ambiguous words to additionally manipulate cognitive challenge. Following each list, participants performed a visual recognition memory task in which they viewed written sentences and indicated whether they remembered hearing the sentence previously. Results: Recognition memory (indexed by d') was poorer for acoustically challenging sentences, poorer for sentences containing ambiguous words, and differentially poorer for noisy high-ambiguity sentences. Similar patterns were observed for Z-transformed response time data. There were no main effects of age, but age interacted with both acoustic clarity and semantic ambiguity such that older adults' recognition memory was poorer for acoustically degraded high-ambiguity sentences than the young adults'. Within the older adult group, exploratory correlation analyses suggested that poorer hearing ability was associated with poorer recognition memory for sentences in noise, and better verbal working memory was associated with better recognition memory for sentences in noise. Conclusions: Our results demonstrate listeners' reliance on domain-general cognitive processes when listening to acoustically challenging speech, even when speech is highly intelligible. Acoustic challenge and semantic ambiguity both reduce the accuracy of listeners' recognition memory for spoken sentences.