Recent technological advances and algorithmic developments make Lattice Quantum Chromodynamics (lattice QCD) a competitive, systematically-improvable method to study hadronic physics from first principles. Lately, there have been many important applications and proposals of using lattice QCD to determine hadronic contributions to various experimentally-well-measured observables to stress-test the Standard Model of particle physics. In this talk, I will present two of such applications: the anomalous magnetic moment of the muon and rare kaon decays. The former is one of the most precisely-measured quantities and is historically the key of our understanding of quantum corrections, whereas the latter provides constraints on the Cabibbo-Kobayashi-Maskawa (CKM) matrix and could potentially be used as a probe for physics beyond the Standard Model.
