Real-time hybrid simulation (RTHS) is a novel testing method that combines numerical simulation and physical testing to evaluate the dynamic performance of engineering structures in large specimens using existing experimental facilities, thus eliminating the scaled effect. In recent years, studies on RTHS have expanded beyond traditional engineering structures, such as wind turbines, automobiles, and ocean structures. Thus far, the dimensions of physical substructures in RTHS are still relatively small, limited by the accuracy of system control for physical systems and the real-time calculation efficiency of numerical simulations. This study summarizes the achievements of real-time numerical simulations for RTHS, including the dimensions of the physical specimen, strategy of numerical simulation, and integral algorithms of RTHS. Meanwhile, two theoretically feasible methods based on parallel computing and surrogate models are discussed, which may be the development trends needed to improve the efficiency and accuracy of numerical solutions in real-time and enlarge the application scope of RTHS.