Abstract-The HiLumi LHC project has as the main objective to increase the LHC peak luminosity by a factor five and the integrated luminosity by a factor ten. This goal will be achieved mainly with a new Interaction Regions lay-out, which will allow a stronger focusing of the colliding beams. The target will be to reduce the beam size in the Interaction Points by a factor of two, which requires doubling the aperture of the low-β (or inner triplet) quadrupole magnets. The use of Nb3Sn superconducting material and, as a result, the possibility of operating at magnetic field levels in the windings higher than 11 T, will limit the increase in length of these quadrupoles, called MQXF, to acceptable levels. After the initial design phase, where the key parameters were chosen and the magnet's conceptual design finalized, the MQXF project, a joint effort between the US LHC Accelerator Research Program (LARP) and CERN, has now entered construction and test phase of the short models. Concurrently, the preparation for the development of the full length prototypes has been initiated. This paper will provide an overview of the project status, describing and reporting on the performance of the superconducting material, the lessons learnt during the fabrication of superconducting coils and support structure, and the fine tuning of the magnet design in view of the start of the prototyping phase.