In practical systems, time-delays inevitably arise when sensors need to measure and require system's data for decision-making as well as when microcontrollers (or other devices) compute the control signal and implement the process. Recently, a great deal of attention has been paid to the study of time-delay problems based on the continuum backstepping control algorithm for its superiority on stability analysis. The main idea of this method is that a first-order hyperbolic transport partial differential equation (T-PDE) is introduced to describe the time-delay phenomenon, and a corresponding time-delay compensated method is developed based on the continuum backstepping control algorithms. This survey summarizes the basic principle and design procedure of the continuum backstepping control algorithm. Besides, recent works of time-delay compensation control based on this algorithm are introduced for time-delay systems including input, output and state time-delay systems. Finally, the future works of the time-delay compensation control based on the continuum backstepping control algorithm are discussed.