ABSTRACT We construct a theoretical framework to study Population III (Pop III) star formation in the post-reionization epoch (z ≲ 6) by combining cosmological simulation data with semi-analytical models. We find that due to radiative feedback (i.e. Lyman–Werner and ionizing radiation) massive haloes ($M_{\rm halo}\gtrsim 10^{9}\ \rm M_{\odot }$) are the major (≳90 per cent) hosts for potential Pop III star formation at z ≲ 6, where dense pockets of metal-poor gas may survive to form Pop III stars, under inefficient mixing of metals released by supernovae. Metal mixing is the key process that determines not only when Pop III star formation ends, but also the total mass, MPopIII, of active Pop III stars per host halo, which is a crucial parameter for direct detection and identification of Pop III hosts. Both aspects are still uncertain due to our limited knowledge of metal mixing during structure formation. Current predictions range from early termination at the end of reionization (z ∼ 5) to continuous Pop III star formation extended to z = 0 at a non-negligible rate $\sim \!10^{-7}\ \rm M_{\odot }\ yr^{-1}\ Mpc^{-3}$, with $M_{\rm PopIII}\sim 10^{3}-10^{6}\ \rm M_{\odot }$. This leads to a broad range of redshift limits for direct detection of Pop III hosts, zPopIII ∼ 0.5–12.5, with detection rates $\lesssim 0.1-20\ \rm arcmin^{-2}$, for current and future space telescopes (e.g. HST, WFIRST, and JWST). Our model also predicts that the majority (≳90 per cent) of the cosmic volume is occupied by metal-free gas. Measuring the volume-filling fractions of this metal-free phase can constrain metal-mixing parameters and Pop III star formation.