CRESST is a direct dark matter search experiment at the deep underground facility of LNGS, designed to measure the nuclear recoil energy from dark matter particles elastically scattering off detector material nuclei. A variety of target crystals such as CaWO4, Al2O3, Si, and LiAlO2 are operated as cryogenic detectors using transition edge sensors (TES) at mK temperatures. In the ongoing CRESST-III measurement campaign, we have operated a 0.35 g Si detector with a nuclear recoil energy threshold of 10 eV, which improved the sensitivity to dark matter particles with masses below 160 MeV /c^2 by up to a factor of 20 compared to previous results. We observe a strong excess of events above the level expected from known background sources at sub-keV energies. Since this energy range is exactly in the region of interest for sub-GeV dark matter searches, understanding this so-called low energy excess is a top priority. Using the Si detector, we have ruled out several hypotheses as dominant contributions, such as noise triggers, radioactive contamination on the crystal surfaces, and scintillation light. This talk will focus on these results from the Si detector. I will also highlight other recent results of CRESST-III and give an overview of its experimental and physics potential for the future.