The book presents the development of the polaron theory and its applications in various fields of physics. Nowadays, methods of the polaron theory are widely used in such sciences as solid state and nuclear physics, chemistry, etc. The monograph includes selected articles, based on the talks, given at the Workshops held in Pushchino in 1993 and 1994. These articles cover different aspects of polaron physics and quantum field theory ranging from nuclear physics to solid state physics and chemistry, they involve both the fundamental research such as bipolarons and the polaron applications to study the self-trapped electron state in various liquids. We hope our book will be of interest to a broad range of readers, which can be able to sense the excitement of the articles.