  The Regge-Wheeler equation describes the axial perturbations of Schwarzschild
metric in linear approximation. We present its exact solutions in terms of the
confluent Heun's functions, the basic properties of the general solution, novel
analytical approach and numerical techniques for study of different boundary
problems which correspond to quasi-normal modes of black holes and other simple
models of compact objects. We depict in more detail the exact solutions of
Regge-Wheeler equation in the Schwarzschild black hole interior and on
Kruscal-Szekeres manifold.
