  This paper reviews the puzzles in modern neutron lifetime measurements and
related unitarity issues in the CKM matrix. It is not a comprehensive and
unbiased compilation of all historic data and studies, but rather a focus on
compelling evidence leading to new physics. In particular, the largely
overlooked nuances of different techniques applied in material and magnetic
trap experiments are clarified. Further detailed analysis shows that the
``beam'' approach of neutron lifetime measurements is likely to give the
``true'' $\beta$-decay lifetime, while discrepancies in ``bottle'' measurements
indicate new physics at play. The most feasible solution to these puzzles is a
newly proposed ordinary-mirror neutron ($n-n'$) oscillation model under the
framework of mirror matter theory. This phenomenological model is reviewed and
introduced, and its explanations of the neutron lifetime anomaly and possible
non-unitarity of the CKM matrix are presented. Most importantly, various new
experimental proposals, especially lifetime measurements with small/narrow
magnetic traps or under super-strong magnetic fields, are discussed in order to
test the surprisingly large anomalous signals that are uniquely predicted by
this new $n-n'$ oscillation model.
