Ultra-high energy cosmic rays (UHECRs) are particles, likely protons and/or nuclei, with energies up to $10^{20}$ eV that are observed through the giant air showers they produce in the atmosphere. These particles carry the information on the most extreme phenomena in the Universe. At these energies, even charged particles could be magnetically rigid enough to keep track of, or even point directly to, the original positions of their sources on the sky. The discovery of anisotropy of UHECRs would thus signify opening of an entirely new window onto the Universe. With the construction and operation of the new generation of cosmic ray experiments -- the Pierre Auger Observatory in the Southern hemisphere and the Telescope Array in the Northern one -- the study of these particles, the most energetic ever detected, has experienced a jump in statistics as well as in the data quality, allowing for a much better sensitivity in searching for their sources. In this review, we summarize the searches for anisotropies and the efforts to identify the sources of UHECRs which have been carried out using these new data.