In this thesis, we develop new models for covariate-varying tail dependence structures and propose novel techniques for fitting these models to both block maxima and threshold exceedances data, under the assumptions of asymptotic dependence and asymptotic independence. Our proposals for the flexible incorporation of covariate influence rely on the (vector) generalized additive modelling infrastructure, and are established in a parametric setting and a non-parametric setting where we develop projection techniques enabling the reduction of the problem of characterizing joint tail dependences to the modelling of univariate random variables. Inference is performed by penalized maximum likelihood estimation combined, when applicable, with censored likelihood techniques. The performance of the resulting estimators is assessed either through simulation studies or based on asymptotic distributions. The developed methodologies are illustrated on environmental datasets where dependence between large events is linked to a set of covariates describing time as well as characteristics of the measurement sites.