The aim of this study is to investigate mathematically the generation and interaction of rogue waves (waves with anomalously high amplitudes relative to the ambient waves) and their impact on wave-energy devices and moving ships. The modelling is demonstrated by analysing variational methods asymptotically and numerically. A reduced potential-flow water-wave model is derived, based on the assumptions of waves with small amplitude and large wavelength. Numerical results obtained using a (dis)continuous Galerkin finite element method (DGFEM) are compared to a soliton splash experiment in a long water channel with a contraction at its end, resulting after a sluice gate is removed at a finite time. The removal of the sluice gate is included in the model through a time-dependent gravitational potential. The water-wave model is also adapted to accommodate nonlinear ship dynamics. The new model consists of the classical water-wave equations, coupled to a set of equations describing the dynamics of the ship. We will first investigate the dynamics of the coupled system linearised around a rest state. For simplicity, we also consider a simple ship structure consisting of V-shaped cross-sections. The model is solved numerically using a DGFEM and the numerical results are compared to observations from experiments in wave tanks that employ geometric wave amplification to create nonlinear rogue-wave effects.