The distribution of the arrival directions of ultra-high energy cosmic rays is, together with the spectrum and the mass composition, a harbinger of their nature and origin. As such, it has been the subject of intense studies at the Pierre Auger Observatory since its inception in 2004, with two main lines of analysis being pursued at different angular scales and at different energies. One concerns the study of the large-scale anisotropy and of its evolution as a function of energy. The technique used is that of the harmonic analysis, performed over all the energy range accessible by the Observatory, from sub-EeV energies to the highest ones. The other line of analysis regards in turn only the arrival directions of the highest energies cosmic rays, namely those above a few tens of EeV: thanks to the high rigidities at play, it aims at the search for anisotropies on (relatively) low angular scales in association with catalogs of plausible astrophysical sources. The talk will review the outcome of such studies after almost 15 years of data taking. It will also illustrate the careful treatment of data as well as the methods used.