  A discussion of the seniority quantum number in many-body systems is
presented. The analysis is carried out for bosons and fermions simultaneously
but is restricted to identical particles occupying a single shell. The emphasis
of the paper is on the possibility of {\em partial} conservation of seniority
which turns out to be a peculiar property of spin-9/2 fermions but prevalent in
systems of interacting bosons of any spin. Partial conservation of seniority is
at the basis of the existence of seniority isomers, frequently observed in
semi-magic nuclei, and also gives rise to peculiar selection rules in
one-nucleon transfer reactions.
