  In some of the physically interesting gauge systems, we show that the
application of the Noether theorem does not lead to the deduction of the
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST charges that obey precisely the
off-shell nilpotency property despite the fact that these charges are $(i)$
derived by using the off-shell nilpotent (anti-)BRST symmetry transformations,
$(ii)$ the generators of the above continuous symmetry transformations, and
$(iii)$ conserved w.r.t. the time-evolution due to the Euler-Lagrange equations
of motion derived from the Lagrangians/Lagrangian densities (that describe the
dynamics of the suitably chosen physical systems). We propose a systematic
method for the derivation of the off-shell nilpotent (anti-)BRST charges from
the corresponding {non-nilpotent Noether conserved (anti-)BRST charges. To
corroborate the sanctity and preciseness of our proposal, we take into account
the examples of $(i)$ the one ($0 + 1$)-dimensional (1D) system of a massive
spinning (i.e. SUSY) relativistic particle, $(ii)$ the D-dimensional
non-Abelian 1-form gauge theory, and $(iii)$ the Abelian 2-form and the
St${\ddot u}$ckelberg-modified version of the massive Abelian 3-form gauge
theories in any arbitrary D-dimension of spacetime. Our present endeavor is a
brief review where some decisive proposals have been made and a few novel
results have been obtained as far as the nilpotency property is concerned.
