GravityCam is a new instrument proposed for the NTT, to perform wide-field high- resolution imaging, which would complement the SOXS spectrograph and enable unique surveys. It will be capable of delivering significantly sharper images from the ground than is normally possible without adaptive optics. Images will be acquired at high speed and aligned before they are combined to yield a 2.5–3-fold improvement in image resolution, giving PSFs with FWHM 0.2-0.3" in typical conditions at La Silla. Science drivers include surveys of planets and satellites down to Lunar mass across the Milky Way via microlensing, weak shear studies of dark matter distribution in distant clusters of galaxies, and multiwavelength follow-ups of background sources that are strongly lensed by galaxy clusters. High-speed photometric data will also be useful for asteroseismology studies, to monitor flaring in accreting compact objects, and to study the Kuiper belt and possibly the Oort cloud via stellar occultations.