AbstractWe present a framework focused on the interdependence of high‐dimensional tail events. This framework allows us to analyse and quantify tail interdependence at different levels of extremity, decompose it into systemic and residual part and to measure the contribution of a constituent to the interdependence of a system. In particular, tail interdependence can capture simultaneous distress of the constituents of a (financial or economic) system and measure its systemic risk. We investigate systemic distress in several financial datasets confirming some known stylized facts and discovering some new findings. Further, we devise statistical tests of interdependence in the tails and outline some additional extensions.