Abstract: Full waveform inversion is an acoustic/elastic/anelastic wave equation-based high accuracy seismic imaging method for studying the Earth's interior structure. To date, it has been widely used in exploration seismology, studies on crustal and mantle structures at both regional and global scales. With this approach, we are able to build a unified theory and algorithm platform to constrain multi-parameter seismic models for the Earth's interior, including P and S wave velocities, anisotropy, attenuation, density and reflectivity, etc. By jointly interpreting these seismic parameters, we hope to better constrain variations in temperature and composition, mantle convection and distribution of water and volatiles. Recent developments include selection of optimal misfit functions, multi-parameter inversion, model regularization, resolution and uncertainty quantification, as well as its applications to special types of datasets, such as ambient-noise recordings and teleseismic scattered waves recorded by dense linear arrays. Furthermore, in order to better interpret inverted multi-parameters and investigate related problems in Earth sciences, we need collaboration among different disciplines, such as synthesizing results from seismology, mineral physics and geodynamic modeling. These results enable us to better understand reservoirs, basin structures, fault distribution and mantle convection.