In December 2015, 195 countries agreed in Paris to hold the increase in global mean surface temperature (GMST) well below 2.0 °C above pre-industrial levels and to pursue efforts to limit the temperature increase to 1.5 °C. Since large financial flows will be needed to keep GMSTs below these targets, it is important to know how GMST has progressed since pre-industrial times. However, the Paris Agreement is not conclusive as regards methods to calculate it. Should trend progression be deduced from GCM simulations or from instrumental records by (statistical) trend methods? Which simulations or GMST datasets should be chosen, and which trend models? What is pre-industrial and, finally, are the Paris targets formulated for total warming, originating from both natural and anthropogenic forcing, or do they refer to anthropogenic warming only? To find answers to these questions we performed an uncertainty and sensitivity analysis where datasets and model choices have been varied. For all cases we evaluated trend progression along with uncertainty information. To do so, we analysed four trend approaches and applied these to the five leading observational GMST products. We find GMST progression to be largely independent of various trend model approaches. However, GMST progression is significantly influenced by the choice of GMST datasets. Uncertainties due to natural variability are largest in size. As a parallel path, we calculated GMST progression from an ensemble of 42 GCM simulations. Mean progression derived from GCM-based GMSTs appears to lie in the range of trend–dataset combinations. A difference between both approaches appears to be the width of uncertainty bands: GCM simulations show a much wider spread. Finally, we discuss various choices for pre-industrial baselines and the role of warming definitions. Based on these findings we propose an estimate for signal progression in GMSTs since pre-industrial.