The search for anisotropies in the arrival directions of ultra-high-energy cosmic rays plays a key role in the efforts to understand their origin. The observed first-harmonic modulation in right ascension above $8\,$EeV, detected by the Pierre Auger Observatory with a current significance of $6.9\sigma$, suggests an extragalactic origin above this energy. Furthermore, there are indications, at the $\sim$$4\sigma$ significance level, of anisotropies at intermediate angular scales, which are obtained when comparing the arrival directions against the distribution of potential sources from astrophysical catalogs, in particular that of nearby starburst galaxies, and around the Centaurus region. In this contribution, we present the status of the different searches for anisotropies at small, intermediate and large angular scales. We use the latest available data set, with 19 years of operation that has yielded $135,000\,$km$^2\,$yr$\,$sr of accumulated exposure, covering the sky at declinations from $-90^\circ$ to $45^\circ$. At small and intermediate scales, we report updates of the all-sky blind search for localized excesses, the study around the Centaurus region, and the likelihood analysis with catalogs of candidate sources. We have also studied the regions of the sky from which the Telescope Array Collaboration has reported hints of excesses in their data and we find no significant effects in the same directions with a data set of comparable size. At large angular scales, the dipolar and quadrupolar amplitudes in energy bins are updated. We discuss the prospects of these searches, both in regards to increases in statistics and in relation to the future inclusion of event-by-event mass estimators in these analyses through the upgrade of the Observatory, AugerPrime.