This review paper is devoted to the understanding of free-electron lasers (FEL) as devices for fundamental physics (FP) studies. After clarifying what FP stands for, we select some aspects of the FEL physics which can be viewed as fundamental. Furthermore, we discuss the perspective uses of the FEL in FP experiments. Regarding the FP aspects of the FEL, we analyze the quantum electrodynamics (QED) nature of the underlying laser mechanism. We look for the truly quantum signature in a process whose phenomenology is dominated by classical effects. As to the use of FEL as a tool for FP experiments we discuss the realization of a device dedicated to the study of non-linear effects in QED such as photon-photon scattering and shining-through-the-wall experiments planned to search for dark matter candidates like axions.