Novel unusual effects in superconductor-ferromagnet (S/F) heterostructures are discussed. The main attention is paid to the triplet component of the superconducting condensate generated in these systems due to the presence of the ferromagnet. This component is odd in frequency and even in the momentum, which makes it insensitive to non-magnetic impurities. The triplet component is not destroyed even by a strong exchange field and can penetrate the ferromagnet over long distances. It is generated as soon as the magnetic moment of the ferromagnet is not homogeneous in space, which can be made experimentally in a controllable way. What is important, the odd triplet component is generated in the conventional s-wave and d-wave superconductors put into a contact with the ferromagnets. In the latter case, the ferromagnet can even enhance the superconductivity. The generation of superconductivity in the strong ferromagnet is not the only unusual effect. In its turn, the ferromagnet moment can be induced in the superconductor on distances of the order of the superconducting coherence length, which may be classified as the inverse proximity effect. We review recent experiments where the long range penetration of the superconductivity through a strong ferromagnet and the inverse proximity effects have been observed.