Single-phase high-frequency resonant inverters (SPHFRIs) with high power density, fast dynamic response, and high energy conversion efficiency have been widely studied and used in academia and industry. With the development of the modularization concept, the operation of multiple inverter modules is desirable because it can remove the limitations of cost, heat dissipation, and component volume in single inverter operation. However, a critical challenge in multiple inverter systems is that the both the phase and magnitude of the output voltage of each inverter module must be controllable to eliminate circulating currents between inverter modules. Great efforts have been made to solve this problem from three aspects: topology, modulation, and control strategy. In this paper, modulation strategies and topologies of different inverters are presented and reviewed to provide guidance to researchers working in this field. Firstly, multiple inverter system based on the SPHFRI is described and its advantages and disadvantages are analyzed. An important issue in the study of multiple inverter systems is presented, that is, the suppression of circulating current. Secondly, the circulating currents in a multiple inverter system are analyzed and derived from two aspects: (1) magnitude and phase angle and (2) active and reactive currents. Thirdly, the inverters used in the multiple inverter system are introduced, and their operating principles, advantages, and disadvantages are reviewed. A key comparison of several inverters is presented for the benefit of the readers. Fourth, through PI closed-loop simulation, the performance of different multiple inverter systems for suppressing the circulating current is compared in two situations: (1) with magnitude discrepancy only and (2) with both magnitude and phase discrepancy. Finally, the advantages and disadvantages of each inverter are summarized, and the state of the art and future trends are presented.