Recent progress regarding multiple spacecraft crossings of the heliospheric current sheet (HCS) is reviewed and placed in the context of streamer belt and heliospheric plasma sheet structure. Historically, multiple crossings have been attributed to waves on the HCS surface. Mounting evidence, however, argues against that view. Most notably, recent application of a heat flux polarity test to 47 cases of multiple crossings in the ISEE 3 data set rules out the possibility that they were caused by the HCS folded back on itself. More than half of these cases contained counterstreaming electrons indicating association with coronal mass ejections (CMEs), and the remaining cases lacked the heat flux pattern required for a folded current sheet. An alternative explanation of the non-CME associated multiple crossings in terms of multiple current sheets is consistent with the data but in a turbulent rather than laminar form. The data suggest passage through a network of tubular current sheets constituting the walls of tangled flux tubes. Multiple HCS crossings are associated with multiple plasma sheet crossings and occur on a hierarchy of scale sizes. These may reflect the hierarchy of scale sizes of transient outflow observed in the streamer belt near the Sun.