Manipulating textile objects in a versatile way remains a challenging problem in robotics, triggered by applications in assistive and industrial domains. The vast number of degrees of freedom involved in deformations undermines the effectiveness of the modelling, planning and control methods available for rigid objects. Within the CLOTHILDE project ( https://clothilde.iri.upc.edu/ ), we have combined geometrical and physical modelling to represent cloth states with reinforcement learning and model-predictive control to endow robots with dynamic manipulation skills. Regarding the former, we defined a taxonomy of grasps and characterized macro-states of textiles by encoding task-relevant cloth-configuration changes, so as to enable planning in the resulting state-graph to accomplish a task. Dynamic cloth manipulation has been attained through learning by demonstration and reinforcement learning, and then applying model-based control by modelling cloth dynamics as that of an inextensible surface. Some robot prototypes equipped with these skills will be shown in the talk, highlighting the design of grippers with specific cloth-handling functions, and the use of virtual reality for collecting data in learning approaches. The work of a highly interdisciplinary team is acknowledged, including mathematicians, computer scientists, mechanical, industrial, telecommunication, and software engineers, as well as a philosopher dealing with the ethical deployment of assistive robots.