Experiments on the effects of humidity in adhesion between rough surfaces have shown that the adhesion energy remains constant below a critical relative humidity (RHcr) and then abruptly jumps to a higher value at RHcr before approaching its upper limit at 100% relative humidity. A model based on a hierarchical rough surface topography is proposed, which quantitatively explains the experimental observations and predicts two threshold RH values, RHcr and RHdry, which define three adhesion regimes: (1) RH<RHdry, no stable water bridges form between the contacting surfaces; (2) RHdry<RH<RHcr, water bridges form but are confined to the initial solid-solid contact regions; and (3) RH>RHcr, water menisci freely form and spread along the interface between the rough surfaces.