Observing the various anatomical and functional information that spans many spatiotemporal scales with high resolution provides deep understandings of the fundamentals of biological systems. Light-field microscopy (LFM) has recently emerged as a scanning-free, scalable method that allows for high-speed, volumetric imaging ranging from single-cell specimens to the mammalian brain. However, the prohibitive reconstruction artifacts and severe computational cost have thus far limited broader applications of LFM. To address the challenge, in this work, we report Fourier LFM (FLFM), a system that processes the light-field information through the Fourier domain. We established a complete theoretical and algorithmic framework that describes light propagation, image formation and system characterization of FLFM. Compared with conventional LFM, FLFM fundamentally mitigates the artifacts, allowing high-resolution imaging across a two- to three-fold extended depth. In addition, the system substantially reduces the reconstruction time by roughly two orders of magnitude. FLFM was validated by high-resolution, artifact-free imaging of various caliber and biological samples. Furthermore, we proposed a generic design principle for FLFM, as a highly scalable method to meet broader imaging needs across various spatial levels. We anticipate FLFM to be a particularly powerful tool for imaging diverse phenotypic and functional information, spanning broad molecular, cellular and tissue systems.