The anomalous Hall effect (AHE) is a quantum phenomenon that arises from the interplay of spin-orbit coupling and the topology of electronic states in materials. This review summarizes recent experimental and theoretical studies that have clarified the AHE, distinguishing between intrinsic and extrinsic contributions. The intrinsic AHE is linked to the Berry phase curvature of the electronic band structure and is independent of disorder, while the extrinsic AHE arises from scattering processes such as skew scattering and side-jump. The intrinsic AHE is dominant in metallic ferromagnets with moderate conductivity, whereas the extrinsic AHE dominates in highly conductive materials. The AHE can be understood through three linear response theories: the semiclassical Boltzmann approach, the Kubo formalism, and the Keldysh formalism. These theories have been shown to be equivalent in the metallic regime. The review also discusses the experimental studies of the AHE in various materials, including transition metals, transition-metal oxides, spinels, pyrochlores, and dilute magnetic semiconductors. These studies have revealed systematic trends in the AHE, with the intrinsic AHE being prominent in materials with strong spin-orbit coupling. The review concludes with a discussion of the current understanding of the AHE and highlights the remaining challenges and future directions in the field.The anomalous Hall effect (AHE) is a quantum phenomenon that arises from the interplay of spin-orbit coupling and the topology of electronic states in materials. This review summarizes recent experimental and theoretical studies that have clarified the AHE, distinguishing between intrinsic and extrinsic contributions. The intrinsic AHE is linked to the Berry phase curvature of the electronic band structure and is independent of disorder, while the extrinsic AHE arises from scattering processes such as skew scattering and side-jump. The intrinsic AHE is dominant in metallic ferromagnets with moderate conductivity, whereas the extrinsic AHE dominates in highly conductive materials. The AHE can be understood through three linear response theories: the semiclassical Boltzmann approach, the Kubo formalism, and the Keldysh formalism. These theories have been shown to be equivalent in the metallic regime. The review also discusses the experimental studies of the AHE in various materials, including transition metals, transition-metal oxides, spinels, pyrochlores, and dilute magnetic semiconductors. These studies have revealed systematic trends in the AHE, with the intrinsic AHE being prominent in materials with strong spin-orbit coupling. The review concludes with a discussion of the current understanding of the AHE and highlights the remaining challenges and future directions in the field.