Prism manifolds are spherical 3-manifolds with D-type finite fundamental
groups. They can be parametrized by a pair of relatively prime integers p>1
and q. The realization problem of prism manifolds asks which prism manifolds
can be obtained by positive Dehn surgery on a knot in S^3. This problem has
been solved in the cases q<0 and q>p. We will discuss the basic idea of the
proof. This talk is based on joint work with Ballinger, Hsu, Mackey, Ochse
and Vafaee, and with Ballinger, Ochse and Vafaee.