Presented at the 2013 SMOS-Aquarius Science WorkshopThe European Space Agency's Soil Moisture and Ocean Salinity (SMOS) mission has provided nearly continuous global record of fully polarimetric brightness temperatures at L-band (1.4135 GHz) since November 2009. The single payload of the SMOS satellite, MIRAS, is a two-dimensional aperture synthesis radiometer that measures the cross-correlations between the signals from many L-band antennas distributed in a Y-shape array. These cross-correlations are transformed by ground processing into brightness temperature images that extend over a swath several hundred kilometers across. Over the ocean, these brightness temperature images are used, together with a forward model of the L-band scene brightness, to derive maps of surface salinity over the global oceans, with full earth coverage approximately every five days.Over the global oceans the surface salinity varies between about 32 and 38 on the practical salinity scale, with the strongest variations in the vicinity of river outflows and heavy rainfall. The sensitivity of the brightness temperature at L-band to a change in salinity depends somewhat upon polarization and sea surface temperature but, in tropical latitudes, is about +1 K in the first Stokes parameter per unit decrease of salinity on the pratical salinity scale. Thus, the dynamic range of L-band brightness temperatures over the open ocean is only several kelvin. As one goal of the mission is to produce global maps of salinity with an accuracy of 0.1 after averaging over 10-30 days, strict requirements must be placed upon the accuracy and stability of the brightness temperatures. Efforts to reach this goal continue, but challenges related to interannual, seasonal, and orbital stability of the retrieved salinity remain. These challenges stem from difficulties in the instrument calibration, image reconstruction, and modeling of the scene brightness over the ocean. On the one hand, the instrument calibration and image reconstruction are plagued by the sun which impacts the accuracy of the brightness temperatures indirectly, through variations in the thermal characteristics of the instrument, and directly, through its impact on the visibilities. On the other hand, the scene modeling is plagued by emission from the rough ocean surface, emission from foam, and galactic radiation scattered towards the instrument by the wind-roughened ocean surface. Moreover, the sun-synchronous orbit of the SMOS satellite is such that both the solar (direct and indirect) and galactic impacts exhibit orbital and seasonal cycles that, if not properly accounted for, will contribute to bias in the salinity.A key factor complicating progress is the fact that the aforementioned problems can produce similar bias evolutions, and so disentangling the various sources of bias is difficult. Using open-ocean model solutions for the brightness temperature images as well as the antenna temperatures (which provide the mean brightness temperature level for the images), this paper will examine the spatial and temporal structures observed in the biases over the nearly four years of continuous data. An attempt will be made to exploit the recent oscillatory character of the sun L-band brightness in order to separate the impacts of the sun and scattered galactic radiation. In parallel, improvements in the modeling of the scattering of galactic radiation will be presented, and a comparison will be made with the impact on the brightness temperatures and salinity maps from the Aquarius mission.Finally, recognizing that adequate calibration and forward scene modeling may not be achieved in the near future, the paper will examine practical alternatives to bias correction, with an emphasis on finding an approach that minimizes impact on the range of applications of the SMOS salinity maps.