Large language models (LLMs) are one of the most impressive achievements of artificial intelligence in recent years. However, their relevance to the study of language more broadly remains unclear. This article considers the potential of LLMs to serve as models of language understanding in humans. While debate on this question typically centres around models’ performance on challenging language understanding tasks, this article argues that the answer depends on models’ underlying competence, and thus that the focus of the debate should be on empirical work which seeks to characterize the representations and processing algorithms that underlie model behaviour. From this perspective, the article offers counterarguments to two commonly cited reasons why LLMs cannot serve as plausible models of language in humans: their lack of symbolic structure and their lack of grounding. For each, a case is made that recent empirical trends undermine the common assumptions about LLMs, and thus that it is premature to draw conclusions about LLMs’ ability (or lack thereof) to offer insights on human language representation and understanding.This article is part of a discussion meeting issue ‘Cognitive artificial intelligence’.