Survey Article on the Theory of Recursive Functions?
A nice reference is "Part C" of Handbook of Mathematical Logic edited by Barwise. Part C includes the following chapters:


Herbert B. Enderton, Elements of recursion theory
Martin Davis, Unsolvable problems
Michael O. Rabin, Decidable theories
Stephen G. Simpson, Degress of unsolvability: a survey of results
Richard A. Shore, $\alpha$-recursion theory
Alexander Kechris and Yiannis N. Moschovakis, Recursion in higher types
Peter Aczel, An introduction to inductive definitions
Donald A. Martin, Descriptive set theory


The chapters are of very high quality and written by leading logicians. This handbook will take you quite far into the world of mathematical logic.