Inference of phylogenetic networks from biological sequence data is a challenging problem, with many theoretical and practical questions still unresolved. In this talk, we introduce a novel divide-and-conquer approach for inferring level-1 networks under the network multispecies coalescent model. We first infer the “tree of blobs” of the network, in which all reticulations are collapsed into nodes. We then focus on resolving the multifurcations within this tree, which correspond to the network’s cycles, by determining an optimal cycle structure for each. Once the multifurcations are individually resolved, we combine them to obtain the full network, provided the cycles collectively allow for a rooting to exist. This method will be implemented in the R package MSCquartets, and we demonstrate its effectiveness through both simulated and empirical datasets. Additionally, we discuss some open problems and avenues for future research. This talk is based on joint work with Elizabeth Allman, Hector Baños, and John Rhodes.