Visualizing diverse anatomical and functional traits that span many spatial scales with high spatio-temporal resolution provides insights into the fundamentals of living organisms. Light-field microscopy (LFM) has recently emerged as a scanning-free, scalable method that allows for high-speed, volumetric functional brain imaging. Given those promising applications at the tissue level, at its other extreme, this highly-scalable approach holds great potential for observing structures and dynamics in single-cell specimens. However, the challenge remains for current LFM to achieve a subcellular level, near-diffraction-limited 3D spatial resolution. Here, we report high-resolution LFM (HR-LFM) for live-cell imaging with a resolution of 300-700 nm in all three dimensions, an imaging depth of several micrometers, and a volume acquisition time of milliseconds. We demonstrate the technique by imaging various cellular dynamics and structures and tracking single particles. The method may advance LFM as a particularly useful tool for understanding biological systems at multiple spatio-temporal levels.