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 the 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) Full-waveform joint inversion of ambient noise data and telelseismic P waves to image the subducted slab beneath the central California.