Transformer-based language models have recently achieved remarkable results in many natural language tasks. However, performance on leaderboards is generally achieved by leveraging massive amounts of training data, and rarely by encoding explicit linguistic knowledge into neural models. This has led many to question the relevance of linguistics for modern natural language processing. In this dissertation, I present several case studies to illustrate how theoretical linguistics and neural language models are still relevant to each other. First, language models are useful to linguists by providing an objective tool to measure semantic distance, which is difficult to do using traditional methods. On the other hand, linguistic theory contributes to language modelling research by providing frameworks and sources of data to probe our language models for specific aspects of language understanding. This thesis contributes three studies that explore different aspects of the syntax-semantics interface in language models. In the first part of my thesis, I apply language models to the problem of word class flexibility. Using mBERT as a source of semantic distance measurements, I present evidence in favour of analyzing word class flexibility as a directional process. In the second part of my thesis, I propose a method to measure surprisal at intermediate layers of language models. My experiments show that sentences containing morphosyntactic anomalies trigger surprisals earlier in language models than semantic and commonsense anomalies. Finally, in the third part of my thesis, I adapt several psycholinguistic studies to show that language models contain knowledge of argument structure constructions. In summary, my thesis develops new connections between natural language processing, linguistic theory, and psycholinguistics to provide fresh perspectives for the interpretation of language models.