The main topic of this research program has been the theory of functional identities and its applications. The foundation of this theory are some about ten years old results that treat some special functional idenities. Over the last few years we have studied functional identities systematically and thereby established a complete theory. In particular, by simplifying the basic method we were able to generalize the results to certain wider classes of rings. Among various applications we point out the fact that using the advanced results on functional identities we have obtained the definitive answers to Herstein's questions on Lie maps in associative rings, that have been open for about 40 years. The fundamentals of the treatment of functional identities in some nonassociative rings have also been established. Some other topics have also been studied. Let us mention the generalizations of the classical density theorem to rings with automorphisms and derivations, an axiomatic approach to the study of elementary operators, contributions to the solutions of the noncommutative Singer-Wermer conjecture, improvements of some known results on linear maps preserving the spectrum (and some related notions), and new results on the Jordan structure in superalgebras.