Much recent work has gone toward computing the ring \(H^*( \text{BDiff}(M)) \) of characteristic classes of smooth fiber bundles with fiber \(M\). For some \(M\) (e.g. surfaces) we have a good understanding of the cohomology in the stable range, but very little is known beyond that. In this talk we will discuss some new characteristic classes that come from the unstable cohomology of arithmetic groups.