Abstract: Numerical earthquake forecasting is one of the outstanding problems in the physics of earthquakes, with significant implications for fundamental science and potential application.Identification of the physical and seismological challenges is one of the critical steps in the approach to numerical earthquake forecast. This article reviews some key issues in the physics and seismology related to numerical earthquake forecasting, including the relation between earthquake rate and stress change, the rate-and-state friction along an earthquake fault, and the transfer of stresses within the Earth. Their significance, status-quo, and future perspectives are discussed.