The review deals with a new range of problems related to the Stark and Zeeman effects in the hydrogen atom, which have attracted a growing interest in these effects during the last decade. These problems include the behavior of a highly excited hydrogen atom in fairly strong electric (F) and magnetic (B) fields. All the parameters describing the behavior of an atom in the fields F and B are considered: changes in the energy levels, lifetimes of the states, intensities (oscillator strengths), decay probabilities, nature of atomic electron trajectories, including the possibility of their stochastization. Both analytic and numerical solution methods are described. Much attention is given to semiclassical and purely classical approaches, which are being developed rapidly. The review is designed to provide a description of the methods without the need to refer to the literature.