Abstract: With the development of satellite technology, low-orbit satellites equipped with high-resolution magnetometers have become an important tool for measuring the Earth's magnetic field, which provides continuous observations around the world regardless of ground and low-altitude weather conditions. Currents in the space, particularly the ionospheric currents, are the main source to cause the magnetic field perturbations at ground and the low Earth orbit (LEO) satellite altitudes. In this paper, we briefly introduce the development history of LEO satellites for measuring the Earth's magnetic field, and the in-orbit calibration processes of magnetic data. In addition, the findings and generation mechanisms of ionospheric currents are reviewed, and the methods for reverting ionospheric currents by using the satellite magnetic measurements are introduced in detail. Currents derived from ground-based and satellite magnetic measurements are not always consistent, and sometimes there are significant differences. Reasons to cause such differences may be related to different data sources (e.g., ground-to-satellite, satellite-to-satellite) and the assumptions in inversion algorithms of currents. Based on limited observations, inversion is often based on assumptions about the geometry and location of the currents, that may not fully agree with the real current distributions. Therefore, combination of ground-based and satellite magnetic measurements, through cross-comparison and cross-verification, is an effective way to test and improve the rationality of the assumptions in the ionospheric current inversion algorithms. Establish the theory and method of space weather monitoring based on the combined and fused magnetic field measurements, will greatly improve our understanding of the ionospheric electrodynamics, the state of the magnetosphere, as well as the coupling mechanisms between ionosphere and magnetosphere.