We propose a type system for reasoning on protocol conformance and deadlock freedom in networks of processes that communicate through unordered mailboxes. We model these networks in the mailbox calculus, a mild extension of the asynchronous pi-calculus with first-class mailboxes and selective input. The calculus subsumes the actor model and allows us to analyze networks with dynamic topologies and varying number of processes possibly mixing different concurrency abstractions. Well-typed processes are deadlock free and never fail because of unexpected messages. For a non-trivial class of them, junk freedom is also guaranteed. We illustrate the expressiveness of the calculus and of the type system by encoding instances of non-uniform, concurrent objects, binary sessions extended with joins and forks, and some known actor benchmarks.