The quantum Hall effect is an old and very rich subject in condensed matter physics. After more than 30 years after the initial discovery, there are new surprising and unexpected phenomena being discovered in this area, both in experiments and in theory. I will focus on the problem of the transitions between plateaux with different values of the Hall conductivity, and the associated critical behavior. The problem still remains a largely unsolved mystery. In this talk I will describe the problem, place it in the context of modern experimental and theoretical developments, and present our recent progress toward its solution.