A floating offshore wind turbine includes a rotor and a generator turned by the rotor. An elongated buoyant body supports a tower that supports the generator and rotor. The buoyant body or the tower may support aerodynamic features to counteract heeling forces or to steer the floating wind turbine as it swings on its anchor line. The floating offshore wind turbine may be configured to move the anchor line force vector to counteract heeling forces. A control system may control the aerodynamic features and the movement of the anchor line force vector.