This paper concerns the nonlinear loading and dynamic response of a heaving rectangular box in two dimensions, using a series of experimental tests in regular and irregular wave conditions. Nonlinear forcing components are found to make major contributions to both the excitation problem and the motion response. Two main sources of nonlinearity are established: the first associated with higher-order wave–structure interactions, and the second associated with viscous dissipation. The present work quantifies the relative influence of these two sources. Adopting a series of regular wave cases, the first source, prevalent in steep wave conditions, is shown to be particularly significant in the diffraction regime, leading to significant excitation force amplifications. In deep water, these nonlinearities are primarily driven by interactions between incident and reflected wave components. The second source, due to vortex shedding, plays a minor role in the excitation problem, but has a major influence on the motion response. Vortex-induced effects are particularly important when the structure exhibits large motions, for example at resonance. To characterise the response in irregular waves, experimental data are provided comprising in excess of 100,000 individual waves, presenting one of the most substantial data sets of this kind to date. In considering these irregular sea states, the two aforementioned sources of nonlinearity are again found to be of critical importance. While wave-induced load amplifications of up to 60% may be observed in the excitation problem, the motion response is primarily governed by vortex-induced attenuations. In order to provide practical engineering solutions, two approaches are offered. For nonlinear forcing predictions, a two parameter Weibull fit is found to be both simple and accurate. In terms of the heave motion, a computationally efficient time-domain simulation, building upon a linear hydrodynamic description and a quadratic MOJS type drag term, leads to good agreement with experimental data.