Axions and axion-like particles (ALPs) appear in many well-motivated extensions of the Standard Model (SM). Their couplings to SM particles can be described in a model-independent way using effective Lagrangians. I will discuss the RG evolution of these couplings from the new-physics scale down to low energies, as well as the first consistent matching of a generic ALP model onto the weak chiral Lagrangian. Phenomenological implications for flavor physics and for the anomalous magnetic moment of the muon will also be presented. Finally, I will describe how even a light ALP necessarily affects the RG evolution of the dimension-6 operators in the SMEFT starting at a high scale, and how this ALP-SMEFT interference can be used to systematically search for indirect ALP effects on precision observables.