Soft continuum robots have been accepted as a promising category of biomedical robots, accredited to the robots’ inherent compliance that makes them safely interact with their surroundings. In its application of minimally invasive surgery, such a continuum concept shares the same view of robotization for conventional endoscopy/laparoscopy. Different from rigid-link robots with accurate analytical kinematics/dynamics, soft robots encounter modeling uncertainties due to intrinsic and extrinsic factors, which would deteriorate the model-based control performances. However, the trade-off between flexibility and controllability of soft manipulators may not be readily optimized but would be demanded for specific kinds of modeling approaches. To this end, data-driven modeling strategies making use of machine learning algorithms would be an encouraging way out for the control of soft continuum robots. In this article, we attempt to overview the current state of kinematic/dynamic model-free control schemes for continuum manipulators, particularly by learning-based means, and discuss their similarities and differences. Perspectives and trends in the development of new control methods are also investigated through the review of existing limitations and challenges.