The class "Theta_2^p" of languages polynomial time truth-table reducible to sets in NP has a wide range of different characterizations. We survey some of them studying the classes obtained when the characterizations are used to define functions instead of languages. We show that in this way the three function classes FP_parallel^NP, FP_log^NP and FL_log^NP are obtained. We give an overview about the known relationships between these classes, including some original results.Postprint (published version
