Low Earth orbit (LEO) satellites have emerged as a primary tool for global geomagnetic field detection and model refinement, owing to their wide coverage, high resolution, and absence of geographical limitations. This paper provides a comprehensive review of the history, key characteristics, measurement accuracy, and future trends in LEO satellite magnetic field measurements. The first part of the paper outlines the evolution of LEO satellites, highlighting their unique advantages. The focus then shifts to the calibration methodology for in-orbit LEO satellite magnetic measurements, with a specific emphasis on vector magnetic field intrinsic calibration and alignment algorithms. Calibration results are presented to demonstrate the effectiveness of these methodologies. In the third section, the paper introduces the theory behind global geomagnetic field modeling. An overview of current global geomagnetic field models is provided, encompassing their sources, spatial resolutions, and other relevant attributes. The paper concludes by presenting the global morphology and features of the main field, lithospheric field, magnetospheric, and ionospheric field. Despite the significant progress enabled by LEO satellite technology, global geomagnetic field modeling faces challenges such as limited spatio-temporal resolution. To address this, incorporating near-surface observation data and continuously optimizing modeling technology are deemed essential solutions.