Several observational facts lead us to expect that the Standard Model (SM) should be extended by new physics (NP) at short distances, but where should we look? We can find clues from several structural puzzles that exist within the SM. One of the few that hints at a low NP scale is the instability of the Higgs mass in the presence of quantum corrections. Another long-standing puzzle is the origin of flavor, or the fact that SM fermions come in three copies. These copies would be physically indistinguishable were it not for the fact that they couple with very different strengths to the Higgs field, hinting at a possible connection between the SM flavor puzzle and the electroweak (EW) hierarchy problem.
Another powerful hint comes from flavor symmetries accidentally respected by the SM. Experimental tests of these accidental symmetries constitute powerful probes of new high-energy dynamics, with current flavor bounds pushing the scale of flavor anarchic NP to the PeV ballpark. This is in apparent contradiction with a natural Higgs mass, which calls for NP not far above the TeV scale. It is therefore plausible to expect that the NP sector responsible for solving the EW hierarchy problem has a very specific flavor structure, again hinting at a possible connection to the SM flavor puzzle. In particular, this would imply new particles around the TeV scale that can distinguish between flavors, just as the Higgs can.
One well-motivated expectation in light of these arguments is TeV scale NP dominantly coupled to the third family, while the couplings to light fermions have a SM Yukawa-like suppression. Under such a hypothesis, the largest NP effects are expected in purely third-family or 3->2 processes. Following this logic, I outline the most promising semi-leptonic channels for flavor factories and emphasize the connection with other low-energy observables, as well as with high-pT searches at the LHC. Finally, I discuss a concrete model where hints of LFU violation observed in semi-leptonic b->c decays can be explained due to the presence of a TeV scale vector leptoquark with a coupling structure reminiscent of the SM Yukawas.