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Grid-forming (GFM) inverters are recognized as a viable solution to increase the penetration of renewable energy in bulk power systems. However, they are physically different from synchronous generators in terms of overcurrent capability. To protect the power semiconductor devices and support the power grid under severe symmetrical disturbances, the GFM control systems should be able to achieve the following requirements: current magnitude limitation, fault current contribution, and fault recovery capability. Various current-limiting control methods are reported in the literature to fulfill these goals, including current limiters, virtual impedance, and voltage limiters. This paper presents an overview of those methods. Emerging challenges that need to be addressed, including temporary overcurrent, unspecified output current vector angle, undesired current saturation, and transient overvoltage, are pointed out. Comparative simulations are conducted to demonstrate the performance of different methods under grid voltage drops and phase jumps. Finally, open issues of current-limiting control methods for GFM inverters, including transient stability assessment, voltage source behavior under overcurrent conditions, and windup of voltage controllers, are shared.