We test three theoretical models of the fast solar wind with a set of remote sensing observations and in-situ measurements taken during the minimum of solar cycle 23. First, the model electron density and temperature are compared to SOHO/SUMER spectroscopic measurements. Second, the model electron density, temperature, and wind speed are used to predict the charge state evolution of the wind plasma from the source regions to the freeze-in point. Frozen-in charge states are compared with Ulysses/SWICS measurements at 1 AU, while charge states close to the Sun are combined with the CHIANTI spectral code to calculate the intensities of selected spectral lines, to be compared with SOHO/SUMER observations in the north polar coronal hole. We find that none of the theoretical models are able to completely reproduce all observations; namely, all of them underestimate the charge state distribution of the solar wind everywhere, although the levels of disagreement vary from model to model. We discuss possible causes of the disagreement, namely, uncertainties in the calculation of the charge state evolution and of line intensities, in the atomic data, and in the assumptions on the wind plasma conditions. Last, we discuss the scenario where the wind is accelerated from a region located in the solar corona rather than in the chromosphere as assumed in the three theoretical models, and find that a wind originating from the corona is in much closer agreement with observations.