The next generation of High Energy Physics particle accelerators is expected to require superconducting dipole magnets with very high magnetic field. For some of the different scenarios under study, arc magnets capable of generating up to 20 T in the bore are considered to maximize the energy of colliding beams. This magnetic field level goes beyond the limits of the traditional superconducting materials used in accelerator magnets, namely the Low Temperature Superconductors Nb-Ti and Nb₃Sn, and requires the use of so-called High Temperature Superconductors, like REBCO and Bi2212. The US Magnet Development Program (MDP) is currently designing and fabricating superconducting dipole magnets in hybrid configuration, i.e. characterized by HTS coil inserts surrounded by Nb₃Sn outserts, with the ultimate goals of reaching a bore field of 20 T. In this paper we discussed the challenges of hybrid magnets in terms of magnetic design, mechanical integration, and quench protection, and we summarize the recent activities carried by the MPD collaboration aimed at the construction of HTS inserts and LTS outserts, first tested in stand-alone configuration, and then assembled and powered in hybrid configuration. In addition, the conceptual study of a future 20 T hybrid magnets is presented, and different possible lay-outs are analyzed.