A question I get quite often is how well the global climate models have been able to predict our present climate as well as making predictions forward in time. Here is an interesting article which looks at several well-known past climate model predictions to see how well they predicted our current climate. What the analysis shows is that, although there is some variation from one model to another based on assumptions the modelers made, the results are generally quite skillful and the predictions that were made were reasonably close to the actual climate. Since climate models are all fundamentally based on energy balance with adjustments for how they depict clouds, ocean circulation, etc. it is not surprising that they get results that are close to what was observed. You can read the details of the comparisons at Carbon Brief here.