The DEMO plant will demonstrate by mid century the feasibility of electric power generation by nuclear fusion. Since 2011, conceptual design studies are coordinated by the EFDA Power Plant Physics and Technology (PPPT) Division, with the aim of identifying requirements, propose design approaches and start R&D for the magnet system of DEMO. The input and generic boundary conditions are given by the system codes: the major radius of the tokamak is about 9m. The proposed operating current at 13.6T peak field is 82 kA, placing the DEMO TF conductor at substantially higher performance compared to ITER TF (68 kA/11.5 T). The innovative winding layout is a graded, layer wound with Nb3Sn/NbTi hybridization, aiming at minimizing the size and the cost of the superconductor. Two options are considered for the Nb3Sn conductor: one a "wind&react" cable-in-conduit (CICC) with reduced void fraction and rectangular shape. The other conductor is a "react&wind" flat cable with copper segregation and thick steel conduit assembled by longitudinal weld. The conductor designs were first drafted in 2012 and updated in 2013 based on a first round of assessments, which includes electromagnetic, thermal-hydraulic and mechanical analysis. The manufacture of full size prototype conductors is planned in 2014. The technical requirement of the DEMO superconducting magnets is highlighted in comparison to ITER and other fusion devices. The large size of the DEMO tokamak is the main challenge for the demonstration of the feasibility of power generation by fusion. Together with the technical issues, the cost of the superconducting magnets will be eventually the crucial aspect to promote the establishment of nuclear fusion as a primary energy source in the coming centuries. (C) 2014 Elsevier B.V. All rights reserved.