The results of the cosmic rays studies, obtained in the AMS experiment during 2011—2015 on the International Space Station, are given. The energy spectra of electrons and positrons at Tev-energies as well as precision measurements of fluxes were performed. The growth with energy of the positron fraction has been observed. Also the proton and Helium spectra have been obtained. A review of theoretical models with possible explanations of the observed phenomena is presented.