With the developments of wireless data communication and network technology, time-delays are widely found in nowadays' control systems, e.g. networked control systems, mobile robot systems, and multiagent systems. Predictor-based control is an effective method dealing with long time-delays because it can generally lead to a delay-free closed-loop system by introducing a prediction for future states. Recently, various predictor-based control methods have been developed for numerous control systems subject to different time-delays, which motivates this survey. This paper presents a comprehensive review of the up-to-date results on the predictor-based control of time-delay systems. Firstly, the ordinary differential equation-based approaches for designing and analysing predictor-based controllers are summarised. Secondly, one reports an alternative method of predictor-based control, in which the systems/controllers are understood in the sense of partial differential equations. Next, several integration-free predictor-based controllers are introduced: by abandoning the infinite-dimensional integral terms, the control laws become easier to realise in practice. Hereafter, the paper discusses the real-time implementations and the practical applications of predictor-based control methods to several particular control systems. Finally, this paper suggests some new trends of predictor-based control for future research.