Let n >= 4 be an even integer and let M_n be the moduli space of n points on P^1 modulo the action of GL(2), thought of as the GIT quotient (P^1)^n/GL(2). The space M_n has a natural projective embedding; let R_n be its projective coordinate ring. The ring R_n was studied classically in the context of invariant theory. In the late nineteenth century, Kempe proved that R_n is generated by its degree one piece. Since that time however, generators for the ideal of relations have not been determined. I will talk about recent work with Howard, Millson and Vakil towards understanding generators of this ideal. Two of our results: 1) the ideal of relations is always generated in degrees <= 3; and 2) for all n not equal to 6 the image of M_n in projective space is cut out by quadrics.