We present recent results on non-invasive beam profile measurement techniques based on Diffraction Radiation (DR) and Cherenkov Diffraction Radiation (ChDR). Both methods exploit the analysis of broadband electromagnetic radiation resulting from polarization currents produced in, or at the boundary of, a medium in close proximity of a charged particle beam. To increase the resolution of DR, measurements were performed in the UV range at a wavelength of 250 nm. With such configurations, sensitivity to the beam size of a 1.2 GeV electron beam below 10 m was observed at the Accelerator Test Facility (ATF) at KEK, Japan. In the case of the ChDR, a proof of principle study was carried out at the Cornell Electron Storage Ring (CESR) where beam profiles were measured in 2017 on a 5.3 GeV positron beam. At the time of writing an experiment to measure the resolution limit of ChDR has been launched at ATF where smaller beam sizes are available. We will present experimental results and discuss the application of such techniques for future accelerators.