Automata theory is mainly concerned with Turing machines and all its relatives-in-spirit. $\lambda$-calculus is rather rarely mentioned in textbooks on automata theory.

What's the common name of the theory mainly concerned with $\lambda$-calculus and its relatives? (I think, "mathematical logic", "computability theory", "programming language theory" and "recursion theory" are too general, compared to "automata theory". But there should be an "$\lambda$-theory", shouldn't it?)