In the last half-decade, the field of natural language processing (NLP) has undergone two major transitions: the switch to neural networks as the primary modeling paradigm and the homogenization of the training regime (pre-train, then fine-tune). Amidst this process, language models have emerged as NLP’s workhorse, displaying increasingly fluent generation capabilities and proving to be an indispensable means of knowledge transfer downstream. Due to the otherwise opaque, black-box nature of such models, researchers have employed aspects of linguistic theory in order to characterize their behavior. Questions central to syntax—the study of the hierarchical structure of language—have factored heavily into such work, shedding invaluable insights about models’ inherent biases and their ability to make human-like generalizations. In this paper, we attempt to take stock of this growing body of literature. In doing so, we observe a lack of clarity across numerous dimensions, which influences the hypotheses that researchers form, as well as the conclusions they draw from their findings. To remedy this, we urge researchers to make careful considerations when investigating coding properties, selecting representations, and evaluating via downstream tasks. Furthermore, we outline the implications of the different types of research questions exhibited in studies on syntax, as well as the inherent pitfalls of aggregate metrics. Ultimately, we hope that our discussion adds nuance to the prospect of studying language models and paves the way for a less monolithic perspective on syntax in this context.