Given a strictly convex n-gon in the plane, at least n-2 diagonals are needed to guarantee "generic global rigidity" (GGR) of the bar framework. Let's call such an object with 2n-2 bars and GGR a polygonal circuit. How rigid are they? Surprisingly, up to n=7, most of them are "universally rigid" in any strictly convex realization! A small fraction of them even have stresses that always have the same signs on all bars in any such realization. What about the ones that are not always universally rigid? Would they always be globally rigid, or at least be "globally rigid" in the space of strictly convex realizations? We present an analog of Cauchy's rigidity in dimension 2 for polygonal circuits. Whether or not any polygonal circuits are flexible is still unknown. I will give examples of polygonal circuits with each type of rigidity, as well as the ones that are unsolved. This is joint work with Robert Connelly, Bill Jackson, and Shin-ichi Tanagawa.