This article gives a summary of recent results on extreme value analysis that were presented at the Journées MAS 2024 in Poitiers. We first set the general background and motivation for these results, and we then discuss partial solutions to four contemporary problems in extreme value analysis: the construction of bias-reduced estimators of the Expected Shortfall (or Tail-Valueat-Risk) at extreme levels, extremal regression and inference in the presence of dependent data, multivariate inference about extreme quantiles using an analogue of the classical ANOVA method in regression, and improved estimation of tail risk measures using nonparametric resampling of multivariate Generalized Pareto distributions.