In view of the preparation for a post-LHC collider, the high-energy physics (HEP) community started from 2010 to discuss various options, including the use of HTS for very high field dipoles. Therefore, a small program was set in Europe aiming at exploring the possibility of using HTS for accelerator quality magnets. Based on various EU funded programs, though at modest levels, has enabled the European community of accelerator magnets to start getting experience in HTS and addressing a few issues. The program was based on use of REBCO tapes to form 10 kA Roebel cables, to be used to wind small dipoles of 30-40 mm aperture in the 5 T range. The dipoles are designed to be later inserted in a background dipole field (in Nb3Sn), to reach eventually a field level in the 16-20 T range, beyond the reach of LTS. The program is currently underway: more than 1 km tape of high performance (Je > 500 A/mm2 at 20 T, 4.2 K has been manufactured and characterized, various 30 m long Roebel cables have been assembled and validated up to 13 kA, a few dipoles have been wound and tested, reaching at present 4.5 T in stand-alone (while a dipole made from race track coils with no-bore exceeded 5 T using stacked tape cable) and a test in a background field is being organized.