This paper presents an approach for data-driven modeling of aeroelasticity and its application to flutter control design of a wind-tunnel wing model. Modeling is centered on system identification of unsteady aerodynamic loads using computational fluid dynamics data, and adopts a nonlinear multivariable extension of the Hammerstein-Wiener system. The formulation is in modal coordinates of the elastic structure, and yields a reduced order model of the aeroelastic feedback loop that is parametrized by airspeed. Flutter suppression is thus cast as a robust stabilization problem over uncertain airspeed, for which a low-order H-infinity controller is computed. The paper discusses in detail parameter sensitivity and observability of the model, the former to justify the chosen model structure, and the latter to provide a criterion for physical sensor placement. Wind tunnel experiments confirm the validity of the modeling approach and the effectiveness of the control design. (C) 2017 Elsevier Ltd. All rights reserved.