Earth System Models (ESMs) have traditionally been assessed for fitness to simulate future climate by evaluating their simulations of the current climate against a suite of observed variables believed to characterize the climate system’s basic features. Such a weak filter on model quality has allowed for a large spread in future climate change to persist in ESM ensembles, making planning for environmental change difficult. Recently an alternative model evaluation technique has arisen, targeting those aspects of current climate that supply information about future changes. "Emergent constraints" (ECs) rely on strong simulated relationships, across an ensemble of different ESMs, between an observable aspect of current climate and future changes. Combining these relationships with contemporary measurements can constrain predictions of those future changes. We discuss the credibility and meaning of ECs that have been proposed. We argue that ECs offer uncertainty reduction when statistical relationships between current and future climate are underpinned by credible mechanisms. As many ECs involve aspects of future climate critical to society, we believe that policy-relevant predictions should consider these constraints, even when mechanisms underpinning the ECs are merely plausible rather than proven. Looking forward, the EC technique may be useful to focus ESM improvement efforts on aspects of climate that matter most for simulation of climate change.  We also believe there are undiscovered ECs relating to climate extremes and teleconnections. Finally, we discuss the possibility that ECs may be used for the critical task of identifying tipping points in the climate system.