  We survey here the construction and the basic properties of descendent
invariants in the theory of stable pairs on nonsingular projective 3-folds. The
main topics covered are the rationality of the generating series, the
functional equation, the Gromov-Witten/Pairs correspondence for descendents,
the Virasoro constraints, and the connection to the virtual fundamental class
of the stable pairs moduli space in algebraic cobordism. In all of these
directions, the proven results constitute only a small part of the conjectural
framework. A central goal of the article is to introduce the open questions as
simply and directly as possible.
