We present a systematic review of 337 articles evaluating the syntactic abilities of Transformer-based language models (TLMs), reporting on over 3,000 datapoints spanning a wide range of syntactic phenomena, languages, models, and methods. We take the data to collectively show that TLMs encode a non-trivial amount of syntactic knowledge. Behavioral evidence shows strong performance on formal syntactic phenomena, but weaker and more variable performance on phenomena at the syntax-semantics interface. Performance is also consistently lower for languages with less digital support. Probing and mechanistic studies further support the presence of syntactic knowledge in TLMs. Yet, because most work remains observational and current approaches are methodologically heterogeneous, insight into the detailed computational mechanisms underlying syntactic processing remains limited. At the same time, the literature remains heavily concentrated on English and BERT-like models. We discuss the implications of our results and provide recommendations for future research.