One of the most important open problems in theoretical physics is a construction of a consistent theory of quantum gravity - a framework capable of describing early universe and processes in strong gravitational fields. An important challenge for quantum gravity comes from the black hole information paradox, a long-standing puzzle which arises from combining general relativity with principles of quantum physics. After reviewing the essence of this paradox, I will describe the progress towards solving it, which happened over the last decade. The approaches presented in the talk are introduced in the framework of string theory. In particular, they are based on the ideas of gauge/gravity duality, which states that gravitational physics has a complementary description in terms of a conventional quantum field theory. I will review the basic ideas of the gauge/gravity correspondence with a particular emphasis on the description of microscopic states contributing to the entropy of a black hole. I will show that such states correspond to regular geometries, and, unlike the familiar metrics appearing in general relativity, these geometries do not have sources. I will also discuss some applications of gauge/gravity duality to the study of dynamical processes, such as Hawking radiation.