The relationships between avian brood parasites and their hosts are widely recognised as model systems for studying coevolution. However, while most brood parasites are known to parasitise multiple species of host and hosts are often subject to parasitism by multiple brood parasite species, the examination of multispecies interactions remains rare. Here, we compile data on all known brood parasite-host relationships and find that complex brood parasite-host systems, where multiple species of brood parasites and hosts coexist and interact, are globally commonplace. By examining patterns of past research, we outline the disparity between patterns of network complexity and past research emphases and discuss factors that may be associated with these patterns. Drawing on insights gained from other systems that have embraced a multispecies framework, we highlight the potential benefits of considering brood parasite-host interactions as ecological networks and brood parasitism as a model system for studying multispecies interactions. Overall, our results provide new insights into the diversity of these relationships, highlight the stark mismatch between past research efforts and global patterns of network complexity, and draw attention to the opportunities that more complex arrangements offer for examining how species interactions shape global patterns of biodiversity.