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International audience; The main purpose of this survey paper is to review the field of convergence between the liquid-propellant rocket-propulsion and automatic-control disciplines. A comprehensive collection of academic works and some industrial developments are summarised and discussed, making the link to the current context of launcher reusability. The main control problem in liquid-propellant rocket engines (LPRE), the target of this survey, generally consists in tracking set-points in combustion-chamber pressure and mixture ratio, their main operating quantities. This goal is attained via the adjustment of flow-control valves while complying with operating constraints. Each aspect of control systems, ranging from modelling to the actual control techniques, is reviewed and subsequently related to the rest of aspects. The comparison of the different approaches points to the general use of linearised models about concrete operating points for deriving steady-state controllers, which in most cases are of PID type. Other more sophisticated approaches present in the literature, incorporating some nonlinear, hybrid or robust techniques, improve certain aspects of performance and robustness. Nevertheless, no fully nonlinear or hybrid frameworks, which may allow the control of a wider throttling domain, have been published. In addition, control during the thermally and structurally demanding transient phases is usually in open loop, and hence with low correction margins. This sort of control enhancements, probably together with more sophisticated monitoring architectures, would serve to extend the life of LPRE, a significant factor in their reusability. Therefore, this survey intends to draw a path for the future control design trends which will certainly be more suitable for reusable LPRE.