The XENON1T was designed to measure nuclear recoil events induced in the interaction of dark-matter particles coming from our galaxy. The detector is based on a dual-phase time projection chamber (TPC) with a 1 ton fiducial mass of liquid xenon in the target. Due to its large mass and ultra-low background, electron recoil event rates were also studied expanding the physics reach. In this talk, I will begin by briefly introducing the detector and its working principle. Interestingly, an excess electron recoil event rate above background is observed below 7 keV with a maximum deviation between 2 and 3 keV. I will describe possibile explanations of this excess rate both from known physics and from searches for new physics. The experiment is being upgraded to XENONnT with a target volume of 6 tons, a fuducial mass of 3 tons and a designed 6-fold lower electron recoil background. XENONnT should allow discriminating between the new physics scenario of the excess events and just unexplained background.