Heavy neutral leptons are attractive candidates for the extension of the Standard Model, since they can explain the physical origin of the three major observable BSM phenomena (Neutrino oscillations, Baryon asymmetry of the Universe, and Dark matter) in framework of one model, where the number of new free parameters is quite small. I will review the role of the new particles in cosmology, their past searches at accelerator facilities, together with the prospects for future searches in the new SHIP experiment (Search for HIdden Particles), that is being actively discussed in CERN.