  The goal of the present article is to survey the general theory of Mori Dream
Spaces, with special regards to the question: When is the blow-up of toric
variety at a general point a Mori Dream Space? We translate the question for
toric surfaces of Picard number one into an interpolation problem involving
points in the projective plane. An instance of such an interpolation problem is
the Gonzalez-Karu theorem that gives new examples of weighted projective planes
whose blow-up at a general point is not a Mori Dream Space.
