The second theorem of Minkowski on successive minima provides optimal upper and lower bounds on the volume of a symmetric convex body in terms of its successive minima. Motivated by conjectures of Mahler and Makai Jr., we study bounds on the volume of a convex body in terms of the successive minima of its polar body. In this talk, we will show the lower bound in the planar case, and the upper bound in the general case. This talk is based on joint work with Martin Henk.