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