Study of the quantum effects originating in intense fields of the different nature – electromagnetic, gravitational, Yang-Mills ones, etc. – is proposed. This includes, in particular, radiation by the charged particles, creation of the electron-positron pairs by ultra-intense fields from vacuum, evolution of neutrino while passing the highly inhomogeneous media, quantum-gravitational effects in cosmology of the early and present Universe, etc. The respective theoretical studies embrace construction of the exact solutions of relativistic wave equations with a definite background, quantization of the field models with an intense background and/or non-linearity in vacuum and in medium in terms of the appropriate quasi-particles, and also general development of the quasi-classical methods in relativistic quantum mechanics, quantum field theory and gravitation. Application of the non-perturbative methods of the quantum field theory with the intense background to the physics of condensed matter, in particular to the physics of graphene and other nanostructures, appears as one of the most topical areas of investigation.