Pulsar Timing Array (PTA) observations have recently gathered substantial evidence for the existence of a gravitational wave background in the nHz frequency band. Searching for anisotropies in this signal is key to determining its origin, and in particular to distinguish possible astrophysical from cosmological sources. In this talk, I discuss the sensitivity of current and future pulsar timing arrays to such anisotropies using the full covariance matrix of pulsar timing delays.