Effective field theory (EFT) and operator product expansion (OPE) are two modern theoretical tools in the realm of particle physics. In this talk, I show these powerful tools can also provide novel and deep insight on understanding short-range features of atomic wave functions. In the first half of the talk, I will start from the simple nonrelativistic Coulomb-Schrodinger EFT, then employ OPE technique to investigate the universal electron-nucleus coalescence behavior of the Schrodinger wave function for an arbitrary atom. An exact OPE relation is proved to all orders in perturbation theory. Our formalism can be readily extended to ascertain the multi-particle coalescence behaviors of atomic wave functions, which are otherwise difficult to achieve from the nonperturbative Schrodinger equation approach. In the second part of my talk, I will illustrate how to solve a 90-year-old puzzle in relativistic wave mechanics, which is related to the renowned Klein-Gordon equation and Dirac equation with a Coulomb potential, from the angle of EFT, OPE and renormalization group equation. In particular, I will demonstrate that, somewhat counterintuitively, the peculiar weakly divergent coalescence behaviors of the Klein-Gordon and Dirac wave functions for a S-wave hydrogen atom, can be best understood in the framework of a nonrelativistic EFT supplemented with certain types of relativistic corrections.