Hybrid simulation (HS) is an experimental testing technique widely used for performance evaluation of structural systems such as large buildings and bridges subjected to earthquake loading. While HS testing has demonstrated to be an efficient and cost-effective alternative to shaking table tests, especially for large structural systems with rate-dependent behavior, accurate and stable results from this methodology are highly dependent on the test specimen, loading equipment, and controller design for dynamic compensation. This lecture presents the fundamentals of HS testing, starting from a brief overview of different HS techniques. Then, the basic framework will be explained, which is based on the classical concept of substructure modeling. Next, a discussion on the effects of laboratory equipment, commonly known as transfer system dynamics, over the accuracy and stability of HS tests will be explained. Subsequently, the real-time hybrid simulation (RTHS) technique will be described. Later, a study is presented on the accuracy and stability of model-based compensation (MBC) approaches for the implementation of a real-time hybrid simulation benchmark problem. The controller architecture is based on feedforward compensator, designed for reference tracking, while a feedback regulator provides improved robustness for undesired disturbance and sensor noise. The results provide evidence of the improved performance of MBC controllers compared to benchmark results. Moreover, the MBC controllers surpass the benchmark controller in terms of robustness, when multiple partitioning cases and control plant uncertainty are considered in the numerical simulations.