Uncertainties about how tropical low clouds respond to climate change are principally behind the uncertainties in climate change projections. If low cloud cover increases as the climate warms, the increased planetary albedo implies a damping feedback on climate changes; if low cloud cover decreases as the climate warms, the reduced albedo implies an amplifying feedback. Existing theories and climate models do not even agree on the sign of low-cloud cover changes as the climate warms, much less on the magnitude. Observations can now constrain the sign of the low-cloud feedback, but do not cover a sufficiently long period to constrain its magnitude well. To constrain and understand cloud feedbacks, we use a hierarchical modeling framework in which large-eddy simulations (LES), validated with data for the present climate, are driven on the large scale by environmental conditions derived from observations or climate model simulations. Insights gained from such climatically relevant LES are then used to infer mechanisms and the magnitude of the low-cloud response to climate change. The result is that low-cloud feedback is robustly positive, with a magnitude likely in the upper half of that simulated by current climate models.