Recent pulsar timing array (PTA) observations provide evidence for a common-spectrum process with emerging spatial correlations, consistent with a gravitational-wave background (GWB). While its origin remains uncertain---ranging from supermassive black hole binaries to cosmological sources---the signal is currently consistent with isotropy, with no confirmed detection of anisotropies. However, effects such as large-scale structure, Poisson fluctuations from a finite number of sources, and line-of-sight projection can induce anisotropies, particularly in an astrophysical background, making them a promising probe of the signal's origin.
In this talk, I will briefly review methods for mapping the angular distribution of GWB intensity with PTAs and present recent results addressing two key questions. First, assuming a statistically isotropic universe, I will examine how anisotropies affect the recovery of the Hellings-Downs correlation curve when used as a validation tool without explicitly modeling anisotropy. Second, I will discuss how the non-uniform sky response of PTAs leads to mode suppression and multipole coupling. In practice, analyses rely on truncating spherical harmonic expansions at a finite angular scale, often chosen to equal the number of distinct pulsar pairs in an array, Npair, following the counting argument that cross-correlations provide at most Npair independent constraints. Commonly used truncations at low multipoles fail to capture all the information available in the array, leading to leakage-induced bias in the reconstructed angular power spectrum. This necessitates truncating analyses at higher multipole, determined by the pulsar positions on the sky rather than solely by Npair. However, extending to higher multipoles renders the inverse problem ill-conditioned, requiring regularization techniques such as truncated singular value decomposition. Even with these approaches, only a limited number of angular modes can be robustly constrained, highlighting an intrinsic trade-off between bias reduction and statistical uncertainty in anisotropy reconstruction.