In recently years there has been a significantly growing
interest in the algebraic spectral analysis of matrices
in the form A = [  F   B';  B  -C  ],
and of their preconditioned versions P^{-1} A$, with
the nonsingular matrix $P$ specifically chosen.
In a variety of applications,  this structure stems from
the discretization of saddle point problems, so that the
matrices F, B, C inherit relevant spectral properties.
In this talk we review some of the results in
the literature, with special emphasis on
aspects that need be taken into account when designing
structured preconditioners for a Krylov subspace system solver.