Due to special relativity, the spin of an electron can couple to its motion. This effect occurs most strongly in materials with large atomic numbers, where the coupling often leads to qualitatively new phenomena such as band inversion in topological insulators and electronic order that spontaneously breaks spatial inversion symmetry. At present, it is unclear what new phases can emerge when spin-orbit coupling is combined with strong electron correlations. We are interested in pursuing this question from an experimental standpoint by investigating what consequences strong spin-orbit coupling imposes on correlated materials.