Modeling the three-dimensional (3D) magnetic fields of the solar active region across multiple layers is crucial for understanding the nature of solar eruptions. The main approach is to extrapolate the magnetic field from magnetograms measured in the photosphere into chromosphere and corona. In the past few decades, a prevailing extrapolation technique, known as force-free field (FFF) extrapolation, assumed a complete neglect of all plasma effects. While the force-free assumption is well justified in the inner solar corona, it is not the case in the photosphere and chromosphere. To better describe the lower solar atmosphere, a non-force-free state called magnetohydrostatic (MHS) equilibrium, which takes into account plasma forces, has gained prominence and witnessed rapid development in recent years. Several tests have demonstrated that the MHS extrapolation yields a more accurate reconstruction of the magnetic field compared to FFF extrapolation. Therefore, it helps to enhance our understanding of the initiation of solar eruptions. In this paper, I will provide an overview of various MHS extrapolation methods, including their most common model assumptions, tests, and most importantly, applications to studies of solar activities.