  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.
  However, specification of joint extremes in design criteria has often been
somewhat \textit{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. Several applications using the
new methods are presented.
