Inertia effect should be considered in ferromagnet magnetization dynamics on a sub picosecond-to-femtosecond-time scale. The inertia effect can be described by the inertial Landau-Lifshitz-Gilbert equation. This paper mainly introduces some theoretical and experimental developments of ultrafast ferromagnetic resonance, magnetization reversal and inertial spin dynamics. These results will be helpful in better understanding the basic mechanism of ultrafast demagnetization and magnetization reversal, and deepen the understanding of the microscopic mechanism of magnetic inertia. In the end, the development trend of future experimental and theoretical research are also presented.