  We review the analytical prescriptions in the literature to model the 21-cm
(emission line surveys/intensity mapping experiments) and Damped Lyman-Alpha
(DLA) observations of neutral hydrogen (HI) in the post-reionization universe.
While these two sets of prescriptions have typically been applied separately
for the two probes, we attempt to connect these approaches to explore the
consequences for the distribution and evolution of HI across redshifts. We find
that a physically motivated, 21-cm based prescription, extended to account for
the DLA observables provides a good fit to the majority of the available data,
but cannot accommodate the recent measurement of the clustering of DLAs at $z
\sim 2.3$. This highlights a tension between the DLA bias and the 21-cm
measurements, unless there is a very significant change in the nature of
HI-bearing systems across redshifts 0-3. We discuss the implications of our
findings for the characteristic host halo masses of the DLAs and the power
spectrum of 21-cm intensity fluctuations.
