Understanding extreme ocean environments and their interaction with fixed and floating structures is critical for the design of offshore and coastal facilities. The joint effect of various ocean variables on extreme responses of offshore structures is fundamental in determining the design loads. For example, it is known that mean values of wave periods tend to increase with increasing storm intensity, and a floating system responds in a complex way to both variables.Specification of joint extremes in design criteria has often been somewhat ad hoc, being based on fairly arbitrary combinations of extremes of variables estimated independently. Such approaches are even outlined in design guidelines. Mathematically more consistent estimates of the joint occurrence of extreme environmental variables fall into two camps in the offshore industry - response-based and response-independent. Both are outlined here, with emphasis on response-independent methods, particularly those based on the conditional extremes model recently introduced by (Heffernan and Tawn, 2004), which has a solid theoretical motivation. We illustrate an application of the conditional extremes model to joint estimation of extreme storm peak significant wave height and peak period at a northern North Sea location, incorporating storm direction as a model covariate. We also discuss joint estimation of extreme current profiles with depth off the North West Shelf of Australia. Methods such as the conditional extremes model provide valuable additions to the metocean engineer's toolkit. © 2013 Elsevier B.V.