The origin and nature of ultrahigh-energy cosmic rays (UHECRs, E > 1018 eV) is one of the most intriguing unsolved problems of modern astrophysics. This review is dedicated to the current status of research in this field. We describe the largest ongoing experiments carried out at the Pierre Auger Observatory and Telescope Array, at the first orbital detector of UHECRs, that is, TUS, and for the KLPVE and JEM-EUSO orbital telescopes, which are currently being developed. We discuss the latest results on the energy spectrum and mass composition of UHECRs and the relationship between UHECRs on the one hand and ultrahigh-energy neutrinos and photons on the other. Finally, we review the latest results on the anisotropy of the arrival directions of UHECRs, which is a crucially important area of research in the search for astrophysical sources of cosmic rays in the highest energy range.