The critical current density J/sub c/ of PbMo/sub 6/S/sub 8/ (PMS) wires has not reached a value required for industrial applications. However, large intragrain J/sub c/ has been observed, indicating that the grain connections play a dominant role in the J/sub c/ limitation. This behavior is similar to that of high-T/sub c/ oxides, where this limitation is thought to have an intrinsic origin related to their extremely short coherence lengths. But the coherence length of PMS lies between those of conventional superconductors and high-T/sub c/ materials. Therefore, it has been argued that an intrinsic granularity behavior is not expected for PMS and that the observed tendency towards granularity has another origin. Recent results on the phase stability, a possible structural transition, and the degradation of the grain boundaries of PMS point to different possible origins for the J/sub c/ limitation. A critical analysis of these investigations is presented, and their impact on the performance of wires is discussed.