Safe design and operations in offshore engineering depend on quantification of the effects of meteorological and oceanographic (metocean) forcings on structures. These forcings have inherent spatio-temporal variabilities, generating uncertainty in structural response estimates. This thesis develops approaches for the quantification and propagation of metocean uncertainty in offshore engineering. There are two research objectives: firstly, to quantify unknown metocean inputs when little, or no, data are available; and secondly, to propagate uncertain metocean inputs in near-real time through computationally expensive numerical simulations of an offshore structure's response. Each objective is discussed with application to a Floating Production Storage Offloading vessel.