In this talk, I will summarize what is currently known about how LLMs process phenomena in syntax (e.g. agreement, hierarchical structure, syntactic dependencies) and the syntax-semantics interface (e.g. binding and anaphora, negation, ellipsis and filler-gap dependencies). The talk will be based on a systematic review of 300+ articles on the topic that Nora Graichen, Iria De Dios, and I are carrying out at the moment.