One of the most interesting and intensively examined research directions in nuclear physics, i.e., the production and investigation of exotic nuclei in the vicinity of drip-lines is investigated. An historical overview of the development of research area is provided. Methods to produce such nuclei realized at the foremost research facilities in the world, e.g., CERN in Switzerland and GSI in Germany, are described. The critical change of the nuclear structure on approaching proton and neutron drip-lines, as well as the results of experimental studies of neutron- and proton-rich nuclei, the mechanism of neutron halo formation in neutron-rich isotopes of helium, lithium, beryllium, and boron, are discussed. In addition, medical applications of radioactive beams are discussed briefly.