Journals and conferences worry that peer reviews assisted by artificial intelligence (AI), in particular, large language models (LLMs), may negatively influence the validity and fairness of the peer-review system, a cornerstone of modern science. In this work, we address this concern with a study of the prevalence and impact of AI-assisted peer reviews in the context of the 2024 International Conference on Learning Representations (ICLR), a large and prestigious machine-learning conference. Our contributions are threefold. Firstly, we obtain a lower bound for the prevalence of AI-assisted reviews at ICLR 2024 using the closed- and open-source LLM detectors, estimating that at least 15.8% of reviews were written with AI assistance. Secondly, we estimate the impact of AI-assisted reviews on submission scores. Considering pairs of reviews with different scores assigned to the same paper, we find that in 53.4% of pairs, the AI-assisted review scores higher than the human review (p = 0.002; relative difference in probability of scoring higher: +14.4% in favor of AI-assisted reviews). Thirdly, we assess the impact of receiving an AI-assisted peer review on submission acceptance. In a matched study, submissions near the acceptance threshold that received an AI-assisted peer review were 4.9 percentage points (p = 0.024) more likely to be accepted than submissions that did not. Overall, we show that AI-assisted reviews are consequential to the peer-review process and offer a discussion on future implications of current trends.