In view of the preparation for a post-LHC collider, in 2010 the high-energy physics (HEP) community started to discuss various options, including the use of HTS for very high-field dipoles. Therefore, a small program was begun in Europe that aimed at exploring the possibility of using HTS for accelerator-quality magnets. Based on various EU-funded programs, though at modest levels, it has enabled the European community of accelerator magnet research to start getting experience in HTS and address a few issues. The program was based on the use of REBa2Cu3O7−x (REBCO) tapes to form 10 kA Roebel cables 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 Low Temperature Superconductors (LTS). The program is currently underway: more than 1 km of high-performance tape (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 4.5 T in stand-alone (while a dipole made from flat race track coils exceeded 5 T using stacked tape cable), and tests in background field are being organized.