Non-destructive compositional analyses are extremely important in many cultural heritage fields. The use of negative muons (an electron analogue) has seen a resurgence in recent times, with developments occurring at several muon sources. After implanting negative muons into a sample muonic x-rays and gammas are released – these can then be detected to determine the composition of the sample. While similar in principle to X-ray fluorescence, the negative muon technique can analyse deep beneath the surface of the sample. By controlling the muons momentum (or energy) the implantation depth of the muons can be controlled, ranging from 10s of µm to 10s of mm. This means the composition at different depths within the sample can be determined non-destructively. Here we review the technique and its recent applications to numismatics, presenting case studies on Roman gold and silver coinage: the former showing no evidence of surface enrichment, the latter unambiguous evidence.