Large language models (LLMs) are increasingly embedded in everyday decision-making scenarios, altering how people make choices. Despite the seemingly ‘superhuman’ capabilities of LLMs in some domains, there are pitfalls in the decision-making performance of LLMs and they should therefore be used with caution. In this Review, we examine LLM outputs through the lens of dual-process theory and against the backdrop of human decision-making. We detail how in decision-making scenarios, LLMs mimic both System-1-like responses — exhibiting cognitive biases and employing heuristics — and System-2-like responses — slow and carefully reasoned — through specific prompting methods. However, LLM reasoning is not fully analogous to human dual-process cognition. For instance, the ‘cognitive’ biases observed in LLMs often reflect patterns in their training data and LLMs exhibit specific non-human biases, such as hallucinations, that constrain their use in real-world decision-making. Despite these limitations, LLMs have the potential to augment human decision-making when deployed responsibly. Thus, we conclude with recommendations for mitigating biases and improving reliability to enable the deployment of LLMs as effective decision-support systems.