The Sea surface KInematics Multiscale monitoring (SKIM) satellite mission is designed to explore ocean surface current and waves. This includes tropical currents, notably the unknown patterns of divergence and their impact on the ocean heat budget near the Equator, monitoring of the emerging Arctic up to 82.5$(\circ)$N. SKIM will also make unprecedented direct measurements of strong currents, from boundary currents to the Antarctic circumpolar current, and their interaction with ocean waves with expected impacts on air-sea fluxes and extreme waves. For the first time, SKIM will directly measure the ocean surface current vector from space. The main instrument on SKIM is a Ka-band conically scanning, multi-beam Doppler radar altimeter/wave scatterometer that includes a state-of-the-art nadir beam comparable to the Poseidon-4 instrument on Sentinel 6. The well proven Doppler pulse-pair technique will give a surface drift velocity representative of the top two meters of the ocean, after subtracting a large wave-induced contribution. Horizontal velocity components will be obtained with an accuracy better than 7 cm/s for horizontal wavelengths larger than 80~km and time resolutions larger than 15 days, with a mean revisit time of 4 days for of 99\% of the global oceans. This will provide unique and innovative measurements that will further our understanding of the transports in the upper ocean layer, permanently distributing heat, carbon, plankton, and plastics. SKIM will also benefit from co-located measurements of water vapor, rain rate, sea ice concentration, and wind vectors provided by the European operational satellite MetOp-SG(B), allowing many joint analyses. SKIM is one of the two candidate satellite missions under development for ESA Earth Explorer 9. The other candidate is the Far infrared Radiation Understanding and Monitoring (FORUM). The final selection will be announced by September 2019, for a launch in the coming decade.