Magnetic resonance wireless power transfer (WPT) has gradually become a popular research topic of near-field regulation in recent years, with wide applications in the fields of mobile phones, implantable medical devices, electric vehicles, and many other fields. However, several challenges remain to be addressed: near-field coupling, which induces multiple frequency splits and prevents the system from maintaining a fixed operating frequency; coupled arrays, which are susceptible to structural errors and parameter perturbations; current research, which primarily focuses on single-load transmission and has resulted in undeveloped multi-load transmission systems; the direction of transmission, which is difficult to control flexibly. In recent years, photonic artificial microstructures have provided a flexible platform for studying topological physics, arousing significant research interest in their fundamental topological characteristics. The most prominent features of topological structures are their nonzero topological invariant and the robust edge states determined by the bulk-edge correspondence: these features can overcome disturbances caused by defects and disorders. Moreover, by modulating the wave function distribution of topological states, energy can be precisely localized, enabling directional WPT. Therefore, implementing topological modes in WPT systems are of significant scientific importance.

This review summarizes recent researches on topological models for robust WPT, which are divided into three main parts. The first part introduces one-dimensional periodic topological structures, focusing primarily on the significant improvements in transmission efficiency and robustness achieved by utilizing topological edge states in the Su-Schrieffer-Heeger (SSH) model for WPT. Moreover, a composite chain formed by two SSH chains is constructed to realize a higher-order parity-time (PT) symmetric topological model. This approach solves the frequency splitting caused by coupled edge states and exhibits lower power losses in standby mode. The second part discusses several types of aperiodic one-dimensional topological chains. By introducing topological defect states at the interface between two different dimer chains, robust multi-load WPT is achieved. Furthermore, based on the integration of artificial intelligence algorithms, the SSH-like topological model enables more efficient and robust WPT than traditional SSH model. The asymmetric edge states in quasi-periodic Harper chain provide a solution for directional transmission in WPT applications. By introducing nonlinear circuits, this model enables active control of the transfer direction. The third part presents the application of high-order topological corner states in multi-load robust WPT, demonstrating the selective excitation of both symmetric and asymmetric corner modes.

Finally, the application prospects of topological modes in WPT systems are discussed. With the development of new physics, the integration of non-Hermitian physics and topological physics holds great promise for achieving simultaneous energy-information transfer, and is expected to achieve compatible WPT, wireless communication, and wireless sensing within a single system. Such a fusion technology will provide breakthroughs in efficiency, robustness, and multifunctionality for next-generation wireless systems.