Anthropogenically forced climate change signals are emerging from the noise of internal variability in observations, and the impacts on society are growing. For decades, Climate or Earth System Models have been predicting how these climate change signals will unfold. While challenges remain, given the growing forced trends and the lengthening observational record, the climate science community is now in a position to confront the signals, as represented by historical trends, in models with observations. This review covers the state of the science on the ability of models to represent historical trends in the climate system. It also outlines robust procedures that should be used when comparing modeled and observed trends and how to move beyond quantification into understanding. Finally, this review discusses cutting-edge methods for identifying sources of discrepancies and the importance of future confrontations.