The European DEMO is a pulsed device with pulse length of 2 hours. The functions devoted to the heating and current drive system are: plasma breakdown, plasma ramp-up to the flat-top where fusion reactions occur, the control of the plasma during the flat-top phase, and finally the plasma ramp-down. The EU-DEMO project was in a Pre-Concept Design Phase during 2014-2020, meaning that in some cases, the design values of the device and the precise requirements from the physics point of view were not yet frozen. A total of 130 MW was considered for the all phases of the plasma: in the flat top, 30 MW is required for neoclassical tearing modes (NTM) control, 30 MW for burn control, and 70 MW for the control of thermal instability (TI), without any specific functions requested from each system, Electron Cyclotron (EC), Ion Cyclotron (IC), or Neutral Beam (NB) Injection. At the beginning of 2020, a strategic decision was taken, to consider EC as the baseline for the next phase (in 2021 and beyond). R&D on IC and NB will be risk mitigation measures. In parallel with progresses in Physics modelling, a decision point on the heating strategy will be taken by 2024. This paper describes the status of the R&D development during the period 2014-2020. It assumes that the 3 systems EC, IC and NB will be needed. For integration studies, they are assumed to be implemented at a power level of at least 50 MW. This paper describes in detail the status reached by the EC, IC and NB at the end of 2020. It will be used in the future for further development of the baseline heating method EC, and serves as starting point to further develop IC and NB in areas needed for these systems to be considered for DEMO.