Quantum transport is very sensitive to the interference of the quantal phase. The Aharanov–Bohm effect is one of the most prominent examples of it. In ferromagnets, the non-coplanar spin structure gives rise to the analogous effect due to the spin chirality, i.e. the solid angle subtended by the spins. This contributes to the anomalous Hall effect at low temperatures. We present here the theoretical results on the two-dimensional Kagome lattice, which is a typical example of the flat-band ferromagnet. The Berry phase induced by the tilting of the spins opens the band gap, and quantized Hall conductance σxy=±e2/h is realized without external magnetic field. We also discuss the anomalous Hall effect observed in the three-dimensional metallic pyrochlore ferromagnets R2Mo2O7 (R=Nd, Sm, Gd).