In traditional electrophysiology, spatially inefficient electronics and the need for tissue-to-electrode proximity defy non-invasive interfaces at scales of more than a thousand low noise, simultaneously recording channels. Using compressed sensing concepts and silicon complementary metal-oxide-semiconductors (CMOS), we demonstrate a platform with 65,536 simultaneously recording and stimulating electrodes in which the per-electrode electronics consume an area of 25.5??m by 25.5??m. Application of this platform to mouse retinal studies is achieved with a high-performance processing pipeline with a 1?GB/s data rate. The platform records from 65,536 electrodes concurrently with a ~10?µV r.m.s. noise; senses spikes from more than 34,000 electrodes when recording across the entire retina; automatically sorts and classifies greater than 1700 neurons following visual stimulation; and stimulates individual neurons using any number of the 65,536 electrodes while observing spikes over the entire retina. The approaches developed here are applicable to other electrophysiological systems and electrode configurations.