  The Moment-SOS hierarchy initially introduced in optimization in 2000, is
based on the theory of the K-moment problem and its dual counterpart,
polynomials that are positive on K. It turns out that this methodology can be
also applied to solve problems with positivity constraints " f (x) $\ge$ 0 for
all x $\in$ K " and/or linear constraints on Borel measures. Such problems can
be viewed as specific instances of the " Generalized Problem of Moments " (GPM)
whose list of important applications in various domains is endless. We describe
this methodology and outline some of its applications in various domains.
