Abstract
Within both multivariate extreme models and spatial processes, it is important to precisely identify dependencies among extremes. In particular detecting asymptotic independence is fundamental and in a multivariate setting, many authors have proposed measures of extreme dependence/independence with sometimes associated tests. Dependence structures within spatial processes are more complex and very few authors have considered other structures than the max-stable one. In this survey paper some major contributions to inference and modelling for extremal dependencies are presented in multivariate and spatial contexts, including the presentation of recent spatial models allowing asymptotic independence.