On the scale of nanometer to femtometer, there have several puzzles, including neutron lifetime, proton charge radius, and deep Dirac level, etc. With the development of high-intensity laser technologies, lasers today can induce extremely strong electromagnetic (EM) fields. Electrons in deep shells of atoms, as well as the atomic nucleus themself, can be affected by the laser EM fields. This may provide a new experimental platform for studies the physical processes on the femto-to-nanometer scale, where atomic physics and nuclear physics coexist. In this paper, we review possible new opportunities for studying the puzzles on femto-to-nanometer scale with high-intensity lasers.