LHC Run 3 will approximately double the available LHC dataset. This wealth of data will be a huge push forward for the search for beyond the Standard Model (BSM) physics. In this contribution, I will discuss three physics targets for Run 3 from a theory perspective: (i) the search for uncovered BSM signatures, (ii) the search for rare decay processes of Standard Model particles, and the combination of LHC measurements with non-collider measurements. I will illustrate each of these topics by an explicit example: (i) the search for bosonic charged Higgs decays, (ii) the search for rare BSM top-quark decays, and (iii) the search for CP violation in the Higgs sector.