The history of the development and current state of hollow-core optical fibers are reviewed. The basic properties which determine the competitive advantages of hollow-core fibers and promising areas for their practical application are discussed. Recent advances in reducing optical losses and the prospects for telecommunication applications of hollow-core fibers, issues of transporting high-intensity optical radiation, and results on nonlinear compression and the generation of ultrashort pulses in gas-filled hollow-core fibers are reviewed. A separate section is devoted to the latest achievements in the development of gas fiber lasers using both optical radiation and gas discharge for pumping.