We study the gravitational clustering of big bang relic neutrinos onto existing cold dark matter (CDM) and baryonic structures within the flat ΛCDM model, using both numerical simulations and a semi-analytical linear technique, with the aim of understanding the neutrinos' clustering properties for direct detection purposes. In a comparative analysis, we find that the linear technique systematically underestimates the amount of clustering for a wide range of CDM halo and neutrino masses. This invalidates earlier claims of the technique's applicability. We then compute the approximate phase space distribution of relic neutrinos in our neighbourhood at Earth, and estimate the large scale neutrino density contrasts within the local Greisen–Zatsepin–Kuzmin zone. With these findings, we discuss the implications of gravitational neutrino clustering for scattering-based detection methods, ranging from flux detection via Cavendish-type torsion balances, to target detection using accelerator beams and cosmic rays. For emission spectroscopy via resonant annihilation of extremely energetic cosmic neutrinos on the relic neutrino background, we give new estimates for the expected enhancement in the event rates in the direction of the Virgo cluster.