Seismic source modeling is taken to mean the modeling of seismograms to investigate kinematic properties of the earthquake source. Current trends such as the use of other data types (e.g. geodetic measurements of coseismic deformation) and the explicit consideration of source dynamics when modeling seismograms are beginning to blur this definition, but I will adhere to it in this review.
I have divided seismic source modeling into teleseismic, regional, and near-source modeling. Teleseismic modeling has the advantage of global coverage for earthquakes of magnitude 5.5 and larger, but does not provide much more than point-source parameters. Regional-distance modeling has the advantage of a more rapid assessment of earthquake source properties, but is complicated by relatively complex wave propagation. The coverage is also limited to areas of broadband regional networks---typically continental areas of developed countries. Near-source modeling has the potential for detailed imaging of source properties, but very few earthquakes occur in regions with sufficient instrumentation to allow this. I have also included a section on historical earthquakes because of the additional issues that seismologists face in working with pre-WWSSN data and because of the important issues, such as earthquake recurrence, that require historical data. In addition to reviewing the progress in seismic source modeling during the last four years, I have also briefly reviewed some of the progress in understanding earthquake physics and hazards that has come about because of basic research in earthquake source modeling.