Abstract: Low frequency (LF) electromagnetic wave propagation in the geospace environment is not only an important part of space physics and radio wave research, but also has significant value for engineering applications such as LF communication, navigation, and near-Earth environment monitoring. This paper first introduces the basic characteristics of the geospace environment and the propagation characteristics of LF electromagnetic waves in various regions. Then, this paper reviews the historical process of this field, from early empirical observations to the modern multi-satellite and multi-platform joint analysis, alongside the parallel development of numerical simulation techniques. Subsequently, the major numerical calculation methods are introduced, covering ray tracing, full-wave solution, waveguide mode, finite element, and finite-difference time-domain methods. This paper also explores a series of core scientific issues and application scenarios regarding the propagation of LF electromagnetic waves in the geospace environment from both natural and artificial sources of excitation. Finally, a research outlook is proposed in view of the limitations of the current numerical simulation methods, aiming to construct a numerical simulation model of LF electromagnetic wave propagation with cross-scale, multiphysics-coupled and adaptive efficient calculation, which provides solid support for related scientific research and engineering applications.