This volume collects novel contributions to comparative generative linguistics that "rethink" existing approaches to an extensive range of phenomena, domains, and architectural questions in linguistic theory. At the heart of the contributions is the tension between descriptive and explanatory adequacy which has long animated generative linguistics and which continues to grow thanks to the increasing amount and diversity of data available to us. The chapters address research questions on the relation of syntax to other aspects of grammar and linguistics more generally, including studies on language acquisition, variation and change, and syntactic interfaces. Many of these contributions show the influence of research by Ian Roberts and collaborators and give the reader a sense of the lively nature of current discussion of topics in synchronic and diachronic comparative syntax ranging from the core verbal domain to higher, propositional domains. This book is complemented by volume II available at https://langsci-press.org/catalog/book/276 and volume III available at https://langsci-press.org/catalog/book/277.