Seismic tomography is one of the fundamental tools in modern seismology to understand the structure and evolution of our planet. With the advancement of high-performance computing, it has now become practical to use state-of-the-art numerical techniques to study the Earth’s 3-D structures and seismic sources. In this talk, I will briefly review the widely used seismic traveltime tomography based on ray theory and introduce our recent studies in full wave seismic tomography based on spectral-element and adjoint methods (adjoint tomography) on supercomputers. Two main topics will be presented are: (1) Adjoint tomography of three component ambient seismic noise for the study of isotropic and anisotropic crustal structure of southern California suited at the Pacific-North American plate boundary. (2) Plane wave full waveform inversion of high frequency teleseismic body waves for high resolution lithospheric seismic imaging at the Iberia and European collisional plate boundary in Western Pyrenees.