 Section 1 of this entry provides an overview of the foundational developments in logic and mathematics which led to the founding of recursive function theory in the 1930s.  Section 2 surveys different forms of recursive definitions, inclusive of the primitive and partial recursive functions which are most central to the classical development of this subject.  Section 3 provides an overview of computability theory, inclusive of the so-called Recursion Theorem (Section 3.4)—a result which highlights the centrality of recursion to computation in general as well as its relationship to self-reference.  Subsequent updates to this entry will provide an overview of subrecursive hierarchies employed in proof theory and computer science as well as a more comprehensive treatment of contemporary computability theory. 