Volumetric functional imaging of transient cellular signaling and motion dynamics poses a significant challenge to current microscopy techniques, primarily due to limitations in hardware bandwidth and the restricted photon budget within short exposure times. In response to this challenge, we present squeezed light field microscopy (SLIM), a computational imaging method that enables rapid detection of high-resolution three-dimensional (3D) light signals using only a single, low-format camera sensor area. SLIM pushes the boundaries of 3D optical microscopy, achieving over one thousand volumes per second across a large field of view of 550 μm in diameter and 300 μm in depth with a spatial resolution of 3.6 μm laterally and 6 μm axially. Using SLIM, we demonstrated blood cell velocimetry across the embryonic zebrafish brain and in a free-moving tail exhibiting high-frequency swinging motion. The millisecond temporal resolution also enables accurate voltage imaging of neural membrane potentials in the leech ganglion, and in the hippocampus of behaving mice. These results collectively establish SLIM as a versatile and robust imaging tool for high-speed microscopy applications.