What's the minimum number of questions needed to find an unknown number x, if up to e of the answers may be erroneous/mendacious? The basic version of this problem, in which questions admit yes/no answers, was originally posed by mathematicians A. Renyi and S. Ulam and amounts to the task of finding optimal error-correcting codes for the binary symmetric channel with noiseless feedback, first considered by Berlekamp. In recent years the problem has been extensively studied and greatly generalized. Most of the efforts have been towards achieving two goals: 1. extending the classical results to more general type of questions (i.e., to more general channels), 2. reducing the interaction between the Questioner and the Responder (i.e, reducing the use of the noiseless channel). In this talk we shall present new results on above issues that are, to date, the best known.