<p>Linear, weakly, and strongly nonlinear aspects of sea load interaction with floating stationary large-volume structures and ships in finite water depth are discussed. Error analysis is emphasized. State-of-the-art potential-flow methods do not consider the important wavelength change due to wave-current interaction in regular waves. This fact is demonstrated by model tests and numerical calculations and has also consequences in higher-order wave load predictions such as for slowly varying motions of moored structures. CO₂ emission in ocean transport is modelled by a two-time scale method accounting for added resistance, propulsion, and engine dynamics in irregular waves. However, voluntary speed reduction plays a vital role in assessing CO₂ emission. Time efficient numerical methods for ship maneuvering in waves based on a two-time scale method with maneuvering as slowly varying and dominant seakeeping response as rapidly varying need accurate calculations of slowly varying wave-induced added resistance, transverse force, and yaw moment. Green water on deck and slamming are considered as examples of strongly nonlinear hydrodynamic load effects. Slamming should be integrated with the structural response analysis and hydroelasticity may matter. Simplifications in mathematical modelling require physical insight and focus on important response variables.</p>