The results of an analytic and numerical investigation of the structure of the X line during steady state magnetic reconnection in collisionless plasma are presented. The structure of the X line essentially depends on a single dimensionless parameter F, which is a measure of the influx of plasma into the reconnection region. For small F the self-consistent plasma current driven at the X line is small, and the magnetic fields are nearly unchanged from the initial vacuum state. With increasing F the current driven at the X line becomes large, and the dissipation region collapses in the direction of the inflow and elongates along the outflow. For sufficient large F the velocity of the plasma ejected from the X line exceeds the local Alfv¿en velocity. In this regime a fast mode shock forms at the outflow end of the dissipation region which slows the high-velocity outflow plasma to the subsonic flow characteristics of the broader outflow region. Finally, at a critical plasma flux Fc the dissipation region collapses to zero thickness; no steady solutions are found for F>Fc. By matching the energy dissipated at the neutral line with the change in global magnetic energy, a self-consistent equation for F is derived which indicates that F always adjusts so that F<˜c. Predications of reconnection rates and assoicated parameters for the geomagnetic tail are presented which are in reasonable agreement with observations.