Kato homology is a homological invariant designed to measure the failure of local-to-global principles in arithmetic geometry. Starting from the Bloch-Ogus spectral sequence for étale homology, Kato extracted complexes whose terms are built from the Galois cohomology of the residue fields of points. The homology of these complexes detects whether the expected Gersten-type exactness, or equivalently a suitable cohomological Hasse principle, holds for an arithmetic scheme. In particular, the zeroth Kato homology corresponds to unramified cohomology. In this talk, I will introduce the Kato complex through the niveau spectral sequence, and discuss the difficulties one faces when carrying this arithmetic construction over to the case of stacks.