We present some recent advances and improvements in shape parametrisation techniques of interfaces for reduced-order modelling with special attention to fluid-structure interaction problems and the management of structural deformations, namely, to represent them into a low-dimensional space (by control points). This allows to reduce the computational effort, and to significantly simplify the (geometrical) deformation procedure, leading to more efficient and fast reduced-order modelling applications in this kind of problems. We propose an efficient methodology to select the geometrical control points for the radial basis functions based on a modal greedy algorithm to improve the computational efficiency in view of more complex fluid-structure applications in several fields. The examples provided deal with aeronautics and wind engineering.