The equations of state (EOS) and the thermodynamics properties of plasma under high temperature are widely applied to the fields of astrophysics, controllable fusion, weapon design and damage. In this paper we mainly review the theoretical model and computing method of the EOS of hot plasma on different density scales and temperature scales. For an ideal plasma, the interaction between ions can be ignored, the EOS is simple and the theories turn matured. Under the condition of extremely high temperature, ions are ionized completely and the EOSs of ions and electrons can be approximated by the EOS of ideal gas. When the temperature is not very high and ions are just partly ionized, the EOS can be obtained by Saha model or its modified model. When atoms are strongly compressed, the EOS can be calculated by Thomas-Fermi model or its modified model. For the non-ideal plasma, there is a strong coupling between ions. No unified theoretical model can completely describe the interaction between ions at arbitrary density and arbitrary temperature. In principle, the quantum molecular dynamics (QMD) can accurately describe the EOS of plasma in large density range and large temperature range. However, due to the enormous computation and the difficulty in converging, it is difficult to apply QMD to the plasma under high temperature. With simple computing method and small computation, classical molecular dynamics using semi-empirical potential can calculate the EOS accurately at high temperature. However, it will produce great error at lower temperature. It is a simple and effective way to obtain a global EOS by using different theoretical models in different density range and different temperature range and by interpolating in the vacant density range and vacant temperature range.