Emergent constraints are physically explainable empirical relationships between characteristics of the current climate and long-term climate prediction that emerge in collections of climate model simulations. With the prospect of constraining long-term climate prediction, scientists have recently uncovered several emergent constraints related to long-term cloud feedbacks. We review these proposed emergent constraints, many of which involve the behavior of low-level clouds, and discuss criteria to assess their credibility. With further research, some of the cases we review may eventually become confirmed emergent constraints, provided they are accompanied by credible physical explanations. Because confirmed emergent constraints identify a source of model error that projects onto climate predictions, they deserve extra attention from those developing climate models and climate observations. While a systematic bias cannot be ruled out, it is noteworthy that the promising emergent constraints suggest larger cloud feedback and hence climate sensitivity.