The LOFT mission concept is one of four candidates selected by ESA for the M3 launch opportunity as Medium Size missions of the Cosmic Vision programme. The launch window is currently planned for between 2022 and 2024. LOFT is designed to exploit the diagnostics of rapid X-ray flux and spectral variability that directly probe the motion of matter down to distances very close to black holes and neutron stars, as well as the physical state of ultradense matter. These primary science goals will be addressed by a payload composed of a Large Area Detector (LAD) and a Wide Field Monitor (WFM). The LAD is a collimated (<1 degree field of view) experiment operating in the energy range 2-50 keV, with a 10 m2 peak effective area and an energy resolution of 260 eV at 6 keV. The WFM will operate in the same energy range as the LAD, enabling simultaneous monitoring of a few-steradian wide field of view, with an angular resolution of <5 arcmin. The LAD and WFM experiments will allow us to investigate variability from submillisecond QPO's to yearlong transient outbursts. In this paper we report the current status of the project.