Abstract: Low Earth orbit (LEO) magnetic satellites typically operate at altitudes of approximately 400–600 km. This altitude range lies near the peak electron density of the ionospheric F region and serves as a crucial zone that couples the E-region dynamo with magnetospheric dynamical processes. With the deployment of high-precision LEO magnetic missions such as CHAMP, Swarm, China Seismo-Electromagnetic Satellite (CSES) and Macau Science Satellite-1 (MSS-1), inverting the ionospheric current system from in situ magnetic field observations has become a frontier topic in ionospheric electrodynamics. Against this background, this paper systematically reviews the research progress on F-region current systems and the related current inversion methods. First, the major currents in the F region are classified, and their underlying physical driving mechanisms are described. Then, three mainstream analysis approaches based on measured magnetic field data are reviewed: the magnetic curl analysis (Curl-B) method, the spherical harmonic modeling method based on Mie decomposition (poloidal - toroidal), and inversion methods based on equivalent-source models (current sheets/lines). Important scientific findings obtained with these approaches are also summarized. Finally, we provide an in-depth analysis of the main bottlenecks currently faced by these approaches. The magnetic curl analysis method suffers from spatiotemporal aliasing and noise amplification when dealing with multiscale structures. The spherical harmonic inversion method based on modeling faces difficulties in calculating the radial derivatives of the magnetic field under limited satellite observation conditions. In equivalent-source methods, height integration leads to a loss of vertical information, and the associated physical interpretation is non-unique. This paper points out that, at the present stage, the equivalent-source method is currently more suitable as boundary conditions and macroscopic constraints for three-dimensional F-layer current inversion, and for characterizing the overall current closure pattern. To realize a true inversion of the local three-dimensional current density in the F-layer, it may be necessary to effectively combine the Curl-B method with full-component Mie vector spherical harmonic analysis. The paper further proposes that embedding physical driving mechanisms, such as atmospheric tides and solar wind, together with multi-satellite magnetic field gradient tensor, may serve as a key breakthrough for accurately characterizing the three-dimensional distribution and variability of F-region volume current density in the future.