Continuum robots with soft, deformable and multi-degree-of-freedom features can adapt to complex environments and perform tasks flexibly, therefore, gradually reflecting important application values in minimally invasive surgery, deep cavity exploration and other fields. To enable continuum robots to perform tasks dexterously and adaptively in complex environments, their motion control is crucial. Traditional model-based control methods require accurate system modelling, have high environmental and structural requirements, and face real-time and computational complexity challenges. With the continuous development of robotics, model-free control and hybrid-model control have become two important approaches to solve the motion control problems of continuum robots. This review systematically summarizes the current status of research on model-free and hybrid-model control for continuum robots in recent years, and discusses in depth the advantages and disadvantages as well as the challenges of the various methods, so as to provide guidance for the coming followers, and to promote the further development and application of continuum robots.