We present a systematic interpretation of vector boson scattering (VBS) and diboson measurements from the LHC in the framework of the dimension-six Standard Model Effective Field Theory (SMEFT). We consider all available measurements of VBS fiducial cross-sections and differential distributions from ATLAS and CMS, in most cases based on the full Run II luminosity, and use them to constrain 16 independent directions in the dimension-six EFT parameter space. Compared to the diboson measurements, we find that VBS provides complementary information on several of the operators relevant for the description of the electroweak sector. We also quantify the ultimate EFT reach of VBS measurements via dedicated projections for the High Luminosity LHC. Our results motivate the integration of VBS processes in future global SMEFT interpretations of particle physics data.