His book Descriptive Set Theory (North-Holland) is the primary reference for the subject.

He is especially associated with the development of the effective, or lightface, version of descriptive set theory, and he is known for the Moschovakis coding lemma that is named after him.

Moschovakis earned his Ph.D. from the University of Wisconsin–Madison in 1963 under the direction of Stephen Kleene, with a dissertation entitled Recursive Analysis.

In 2015, he was elected as a fellow of the American Mathematical Society "for contributions to mathematical logic, especially set theory and computability theory, and for exposition".

[1] For many years, he has split his time between UCLA and the University of Athens (he retired from the latter in July 2005).