The flavor puzzles remain among the most compelling open questions in particle physics. The striking hierarchies observed in the masses and mixing of charged fermions define the Standard Model (SM) flavor puzzle, a profound structural enigma pointing to physics beyond the SM. Simultaneously, the absence of deviations from SM predictions in precision measurements of flavor-changing neutral currents imposes severe constraints on new physics at the TeV scale, giving rise to the new physics flavor puzzle. This review article provides an overview of a selection of recent advancements in flavor model building, with a particular focus on attempts to address one or both of these puzzles within the quark sector.