I will talk about L1 full groups of ergodic measure-preserving transformations, which are measurable analogues of topological full groups of minimal homeomorphisms of the Cantor space. After describing some of the basic properties of these groups, I will present a short proof that the index map takes values into Z which was found with Todor Tsankov. Finally, I will mention some results on the topological rank of L1 full groups.