Multiparty session types (MSTs) are a type-based approach to reasoning about communication protocols. In the spirit of Andreas Podelski’s lifelong fascination with automata theory and its ability to shed a new light on algorithmic problems in formal methods, I will discuss automata-theoretic algorithms for solving verification, synthesis, and subtyping problems for MSTs. Our results improve upon prior work in terms of generality, completeness, and complexity. The talk is based on joint work with Elaine Li, Felix Stutz, and Damien Zufferey.