Introduced as symmetric types for pi-processes, session types have been developed into a large theory for verification of message-passing programs. Their main principle is as follows: a global type describing the expected interactions inside a network is projected into several local types: if every agent abides to its local type, the whole network abides to the global specification. I will present the Multiparty Session Types theory through recent developments: full-abstract embedding into the pi-calculus, nested protocols, automatic monitor generation, session types with multisession assertions.