A recent trend in seismology has been to model the earthquake source as a dynamically extending shear crack, and several basic concepts which seem to be important in this modeling process are examined. First, the universal spatial dependence of the plane elastodynamic stress and velocity fields near a sharp propagating crack tip is demonstrated for both subsonic and transsonic crack speeds, and the corresponding energy release rates are considered. Next, a class of steady state shear crack propagation problems is analyzed, based on both a direct stress analysis approach and an energy integral approach which obviates the need for a complete stress analysis in some cases. Several distinct stress differences which correspond to some of the common definitions of stress drop are involved in the analysis of these simple problems. Finally, some analytical considerations are presented which are relevant to rupture velocity determination for transient shear crack growth according to various fracture criteria, such as the critical stress intensity factor criterion, the critical energy release rate criterion, and the critical stress level criterion. Possible effects of spatially nonuniform stress drop and frictional resistance on rupture propagation are also discussed.