Solar fluxes at the Earth's surface calculated in General Circulation Models (GCMs) contain large uncertainties, not only in the presence of clouds but, as shown here, even under clear-sky (i.e., cloud-free) conditions. Adequate observations to constrain the uncertainties in these clear-sky fluxes have long been missing. The present study provides newly derived observational clear-sky climatologies at worldwide distributed anchor sites with high-accuracy measurements from the Baseline Surface Radiation Network (BSRN) and the Atmospheric Radiation Measurement Program (ARM). These data are used to systematically assess the performance of a total of 36 GCMs with respect to their surface solar clear-sky fluxes. These models represent almost 2 decades of model development, from the atmospheric model intercomparison projects AMIP I and AMIP II to the state of the art models participating in the 4th Assessment Report of the Intergovernmental Panel on Climate Change (IPCC-AR4). Results show that earlier model versions tend to largely overestimate the surface insolation under cloud-free conditions. This identifies an overly transparent cloud-free atmosphere as a key error source for the excessive surface insolation in GCMs noted in previous studies. Possible origins are an underestimated water vapor absorption and a lack of adequate aerosol forcing. Similar biases remain in a number of current models with comparatively low atmospheric clear-sky solar absorption (around 60 Wm-2 in the global mean). However, there are now several models participating in IPCC-AR4 with higher atmospheric clear-sky absorption (70 Wm-2 and up, globally averaged) and more realistic aerosol treatment, which are in excellent agreement with the newly derived observational clear-sky climatologies. This underlines the progress made in radiative transfer modeling as well as in the observation and diagnosis of solar radiation under cloudless atmospheres and puts the most likely value of solar radiation absorbed in the cloud-free atmosphere slightly above 70 Wm-2.