Computer models are essential tools in the earth system sciences. They underpin our search for understanding of earth system functioning and support decision- and policy-making across spatial and temporal scales. To understand the implications of uncertainty and environmental variability on the identification of such earth system models and their predictions, we can rely on increasingly powerful Global Sensitivity Analysis (GSA)methods. Previous reviews have characterised the variability of GSA methods available and their usability for different tasks. In our paper we rather focus on reviewing what has been learned so far by applying GSA to models across the earth system sciences, independently of the specific algorithm that was applied. We identify and discuss 10 key findings with general applicability and relevance for the earth sciences. We further provide an A-B-C-D of best practise in applying GSA methods, which we have derived from analysing why some GSA applications provided more insight than others.