  The existence of the cosmic neutrino background (CnuB) is a fundamental
prediction of the standard Big Bang cosmology. Although current cosmological
probes provide indirect observational evidence, the direct detection of the
CnuB in a laboratory experiment is a great challenge to the present
experimental techniques. We discuss the future prospects for the direct
detection of the CnuB, with the emphasis on the method of captures on
beta-decaying nuclei and the PTOLEMY project. Other possibilities using the
electron-capture (EC) decaying nuclei, the annihilation of extremely
high-energy cosmic neutrinos (EHEC\nus) at the Z-resonance, and the atomic
de-excitation method are also discussed in this review.
