Airliners carry substantial amounts of fuel inside their wing tanks, causing liquid-structure interaction effects that are not fully understood. Whilst often modelled as frozen mass, the fuel inside wing-integrated tanks can also interact violently with the wing structure, leading to phenomena that may be exploited as a means of passively reducing gust loads and increasing the net damping. Specific to the out-of-plane bending motion of flexible wings, the main liquid excitation direction is vertical and the wing amplitudes can exceed the fuel tank height. The primary aim of this thesis is to analyse the nonlinear dynamic interactions between aircraft wings and the fuel contained inside their built-in tanks following discrete gust-type excitation. To achieve this aim, four experimental campaigns were carried out with gradually increasing complexity and three sloshing numerical models were investigated. The vertical sloshing interaction typical of aircraft wings was isolated as a single degree of freedom and studied under transient liquid-structure coupled conditions and also harmonic excitation. A novel 3m long wing demonstrator with a semi-transparent fuel tank allowing for flow observation was designed, manufactured, and tested. Multiple numerical approaches based on sloshing equivalent mechanical formulations gave good agreement with the experiments. The dependency of damping on filling level and amplitude of excitation was investigated under various excitation conditions with a focus on the highly nonlinear large-amplitude regimes. The optimal filling level where the sloshing damping effect is maximized under vertical excitation was found to be 50% and also the existence of a damping saturation amplitude was demonstrated and systematically evaluated. In-depth sloshing hysteresis cycle analysis showed the relationship between the liquid sloshing patterns and the amplitude and frequency-dependent induced damping. These insights were used to further understand the effects observed in the realistic scaled wing demonstrator. Damping variations similar to those observed in the simpler systems were noted in terms of filling level and excitation amplitude, with particularities due to the added complexity of wings, such as the nonuniform spanwise tank amplitude, tank geometry, or richer frequency content. The spanwise distribution of fuel influences the damping significantly via the varying sloshing root moment arm and local vertical acceleration. The tank baffles were found to have an effect only via their spanwise compartmentalization of the fuel. In the most realistic case considered, with representative baffle geometry and positive dihedral, a damping ratio increase of 2.33% critical damping on top of the structural damping was observed due to violent sloshing immediately after step release. The findings presented here are significant as they indicate means of exploiting the already existing fuel inside wing tanks to increase the net structural damping. The extensive experimental data available is also valuable for the liquid sloshing community for further developments of high and low-fidelity numerical models.