The interest to this problem has started with J. Mather's work on perturbations of Geodesic Flows and is considered to be closely related to the famous problem of Arnold diffusion. Recently we developed a general theory which provides a relatively simple explanation for the energy drift. In the lecture I will give an introduction to the theory of slow-fast Hamiltonian systems, explain the background behind averaging theory and adiabatic invariants, and describe a new mechanism responsible for destruction of adiabatic invariants.