The area of cyclic polygons: Recent progress on Robbins' conjectures

In his works [Discrete Comput. Geom. 12 (1994) 223-236; Amer. Math. Monthly 102 (1995) 523-530] David Robbins proposed several interrelated conjectures on the area of the polygons inscribed in a circle as an algebraic function of its sides. Most recently, these conjectures have been established in the course of several independent investigations. In this note we give an informal outline of these developments.