Cosmic rays are energetic particles coming to the Earth from space. They bombard the atmosphere producing cascades of particles that spread over a large area when they reach the ground. Cosmic ray energies vary in the wide band from about 10 8 eV up to few 10 20 eV. It is established that most particles with energies of ~ (10 8-10 9) eV come from the Sun, cosmic rays with higher energies, up to ~ 10 17-10 18 eV are produced in the Galaxy. In these energy bands, particles are called solar cosmic rays and galactic cosmic rays, respectively. Particles with the highest energies, from approximately 4•10 19 to few 10 20 eV, are called Ultra-High Energy Cosmic Rays (UHECRs). It is likely that they are originated outside the Milky Way. The common argument is that magnetic fields in the Galaxy cannot confine particles at ultra-high energies. Indeed, no significant excess of UHECRs has been observed toward the galactic disk. Still, the hypothesis about extragalactic origin of UHECRs is not confirmed experimentally. The flux of cosmic rays at the Earth decreases rapidly with energy and it becomes very low at ultra-high energies: At the energy E≈10 20 eV the flux equals about 1 particle per year per 100 km 2. Because of this, the only way to detect UHECRs is through their interactions with the Earth's atmosphere. UHECRs produce huge cascades with billions particles which are distributed over areas of ~10-1000 square kilometers. Therefore, giant arrays are operated to detect UHECRs. These are Pierre Auger array having a detection area of 3,000 km 2 , located in Argentina and Telescope array sampling events over almost 780 km 2 in Uta, USA. At arrays particle energies and arrival directions are measured, mass composition and parameters of hadronic interactions at the highest energies can be derived as well. Until now the main problem of UHECRs is where they come from. Many ideas were suggested on this subject. They can be divided into two groups. First, particles, possibly, are accelerated to high energies in various astrophysics objects (active galactic nuclei, powerful radio galaxies, gamma-bursts, etc.). Second, it was expected that UHECRs were produced in top-down scenarios through topological defects or heavy dark matter decays not far from the Earth. In addition, some exotic models were suggested (e.g., micro black holes can exist in the Earth's atmosphere and produce UHECRs).