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The next large-scale collider facility being planned in the US is the Electron-Ion Collider (EIC) at Brookhaven National Lab. The EIC is expected to revolutionize our understanding of the internal structure of the proton and other nuclei. This talk will address two themes in EIC science. We will first study inclusive jet production in electron-proton collisions at the EIC and demonstrate its potential for improving our understanding of polarized PDFs. The second theme will show the potential of the EIC to sharpen our probes of physics beyond the Standard Model in the context of the Standard Model Effective Field Theory (SMEFT). The ability to perform measurements with both polarized electron and proton beams at the EIC provides a powerful tool that can disentangle effects from different SMEFT operators and complements ongoing searches at the LHC.