Free-electron light sources feature extraordinary luminosity, directionality, and coherence, which has enabled significant scientific progress in fields including physics, chemistry, and biology. The next generation of light sources has aimed at compact radiation sources driven by free electrons, with the advantages of reduction in both space and cost. With the rapid development of ultra-intense and ultrashort lasers, great effort has been devoted to the quest for compact free-electron lasers (FELs). This review focuses on the current efforts and advancements in the development of compact FELs, with a particular emphasis on two notable paths: the development of compact accelerators and the construction of micro undulators based on innovative materials/structures or optical modulation of electrons. In addition, the physical essence of inverse Compton scattering is discussed, which offers remarkable capability to develop an optical undulator with a spatial period that matches the optical wavelength. Recent scientific developments and future directions for miniaturized and integrated free-electron coherent light sources are also reviewed. In the future, the prospect of generating ultrashort electron pulses will provide fascinating means of producing superradiant radiation, promising high brilliance and coherence even on a micro scale using optical micro undulators.