Gyrotron R&D within the EUROfusion Work Package Heating and Current Drive (WPHCD) is addressing the challenging requirements posed on gyrotrons by the European concept for a demonstration fusion power plant (EU DEMO). These requirements, as specified within WPHCD, ask for highly reliable and robust long-pulse operation of the gyrotron, delivering 2 MW of microwave power at frequencies above 200 GHz with a high overall efficiency above 60% and the option for fast frequency step-tunability. To meet these targets, which are clearly beyond today's state-of-the-art, the R&D activities within WPHCD are organized in five main branches: these are the experimental verification of the advanced coaxial gyrotron technology at long pulses, the development of a coaxial gyrotron meeting the EU DEMO requirements, the development of multi-stage depressed collectors for enhanced energy recovery, the development of large broadband diamond windows to allow fast frequency tunability of the gyrotron, and the studies on further innovations and improvement of critical gyrotron components, in view of optimization of performance, reliability, and industrialization. The paper presents the progress made on these activities, the recent results, and the near-term planning. The major recent achievements include (i) the experimental validation of the fabrication of the new, water-cooled components for the longer-pulse coaxial gyrotron at Karlsruhe Institute of Technology, by demonstrating 2.2 MW at 170 GHz with 33% efficiency without depressed collector, (ii) the design of key components for a 2 MW, 170/204 GHz dual-frequency coaxial gyrotron, (iii) the design of a two-stage depressed collector with 77% efficiency, (iv) the first-ever production, in an industrial plasma reactor, of large chemical vapor deposition diamond wafers of 180 mm diameter, (v) the procurement of an advanced electron gun with coated emitter edges, and (vi) advances in the theoretical and numerical modelling for investigating improved concepts for the gyrotron beam tunnel and cavity.