Seismic tomography is one of the principal geophysical techniques for determining the three-dimensional (3-D) distribution of physical properties inside the Earth, for those that have an effect on seismic-wave propagation: elastic, anelastic, and anisotropic parameters, and density. We present a comprehensive survey of ‘passive’ (earthquake source) seismic tomography and inversion methods as applied to local-, regional-, and global-scale studies. A review of the data types in seismology sets the stage for the development of the modeling approaches utilized in seismic tomography. We devote sections of the chapter to the critical issues of model parametrization (how we represent the 3-D Earth for computational purposes); model solution (the use of inverse theory to obtain the 3-D model from the data); and model assessment (methods to evaluate the resolution and uncertainty of a tomographic model, as such models are only useful if we know how well they represent the real Earth). We conclude with a brief look at some of the exciting frontier areas of seismic tomography.