Observed changes in the HadCRUH global land surface specific humidity and CRUTEM3 surface temperature from 1973 to 1999 are compared to CMIP3 archive climate model simulations with 20th Century forcings. Observed humidity increases are proportionately largest in the Northern Hemisphere, especially in winter. At the largest spatio-temporal scales moistening is close to the Clausius-Clapeyron scaling of the saturated specific humidity (~7% K -1). At smaller scales in water-limited regions, changes in specific humidity are strongly inversely correlated with total changes in temperature. Conversely, in some regions increases are faster than implied by the Clausius-Clapeyron relation. The range of climate model specific humidity seasonal climatology and variance encompasses the observations. The models also reproduce the magnitude of observed interannual variance over all large regions. Observed and modelled trends and temperature-humidity relationships are comparable except for the extratropical Southern Hemisphere where observations exhibit no trend but models exhibit moistening. This may arise from: long-term biases remaining in the observations; the relative paucity of observational coverage; or common model errors. The overall degree of consistency of anthropogenically forced models with the observations is further evidence for anthropogenic influence on the climate of the late 20th century.