First, derivation of the predicted number density of the cosmic neutrino background (CNB) will be reviewed, and its role in the Hot Big-Bang Cosmology stressed. Next I will discuss the amount of possible density enhancement in galactic clusters of massive, and by now nonrelativistic, CNB neutrinos. The application of coherent scattering to the detection of CNB will be also reviewed, and its difficulties explained. Main part of the talk will be concerned with the detection of CNB using radioactive targets. While such approach is extremely difficult, one can envisage that it might eventually work provided the neutrino mass is sufficiently large, perhaps at least 0.1 eV.