This is a survey of literature on simulation of magnetic reconnection in the presence of the Hall effect. We give a brief description of the Earth's magnetosphere, the ideal and the Hall MHD models, as well as the "traditional" and the "modified" electromagnetic hybrid models. For the Hall MHD we analyze the Hall term in the generalized Ohm's law. We review publications on the modeling of reconnection processes in space plasma that use Hall MHD, PIC simulation, and hybrid simulation. The main focus is on the manifestation of Hall currents. Simulation results using different models are compared. A separate section examines studies on the simulation of current sheet dynamics, which is closely linked with magnetic reconnection.