LiteBIRD is a JAXA-led Strategic Large-Class mission designed to search for the existence of the primordial gravitational waves produced during the inflationary phase of the Universe, through the measurements of their imprint onto the polarization of the cosmic microwave background (CMB). These measurements, requiring unprecedented sensitivity, will be performed over the full sky, at large angular scales, and over 15 frequency bands from 34 GHz to 448 GHz. The LiteBIRD instruments consist of three telescopes, namely the Low-, Medium- and High-Frequency Telescope (respectively LFT, MFT and HFT). We present in this paper an overview of the design of the Medium-Frequency Telescope (89-224 GHz) and the High-Frequency Telescope (166-448 GHz), the so-called MHFT, under European responsibility, which are two cryogenic refractive telescopes cooled down to 5 K. They include a continuous rotating half-wave plate as the first optical element, two high-density polyethylene (HDPE) lenses and more than three thousand transition-edge sensor (TES) detectors cooled to 100 mK. We provide an overview of the concept design and the remaining specific challenges that we have to face in order to achieve the scientific goals of LiteBIRD.
