Magnetic damping refers to the physical parameter describing how the magnetization vector M dissipates energy and eventually returns to its equilibrium orientation after being perturbed. It directly governs energy dissipation and response speed in spintronic devices. Traditionally, magnetic damping is regarded as an isotropic material constant. However, as material systems enter the nanoscale thin-film regime, reduced dimensionality and interface effects break spatial symmetry. Recent theoretical and experimental studies have revealed that the magnitude of magnetic damping strongly depends on the direction of magnetization, prompting a shift from a scalar-to a tensor-based description.

This review systematically surveys research progress in this field from historical development, material systems, physical mechanisms, modulation approaches to characterization methods. Different material systems exhibit different characteristics: the properties of single-layer films are predominantly governed by crystal symmetry, whereas interfacial effects dominate in multilayer films. The physical origin of magnetic damping is jointly determined by intrinsic factors such as electronic density of states and spin-orbit coupling and extrinsic factors including two-magnon scattering and interface effects. Among these, spin-orbit coupling serves as a crucial bridge connecting microscopic electronic structure with macroscopic magnetization dynamics. In terms of modulation techniques, the methods of achieving anisotropic magnetic damping through structural design, fabrication processes, and compositional control have become relatively mature. Regarding characterization, complementary mainstream techniques such as ferromagnetic resonance (FMR) and time-resolved magneto-optical Kerr effect (TR-MOKE) are now widely applied.

In the future, the research on anisotropic magnetic damping should be promoted simultaneously in basic studies such as multiphysics filed coupling and quantum effects, as well as device integration and application exploration, in order to promote the development of next-generation high-performance spintronic devices.