In English and other languages, multiple adjectives in a complex noun phrase show intricate ordering patterns that have been a target of much linguistic theory. These patterns offer an opportunity to assess the ability of language models (LMs) to learn subtle rules of language involving factors that cross the traditional divisions of syntax, semantics, and pragmatics. We review existing hypotheses designed to explain Adjective Order Preferences (AOPs) in humans and develop a setup to study AOPs in LMs: we present a reusable corpus of adjective pairs and define AOP measures for LMs. With these tools, we study a series of LMs across intermediate checkpoints during training. We find that all models' predictions are much closer to human AOPs than predictions generated by factors identified in theoretical linguistics. At the same time, we demonstrate that the observed AOPs in LMs are strongly correlated with the frequency of the adjective pairs in the training data and report limited generalization to unseen combinations. This highlights the difficulty in establishing the link between LM performance and linguistic theory. We therefore conclude with a road map for future studies our results set the stage for, and a discussion of key questions about the nature of knowledge in LMs and their ability to generalize beyond the training sets.