Evidence from 184 countries over the span of 25 years is gathered and analyzed to understand North–North, South–South, and North–South international migration flows. Conceptually, the analysis borrows from network theory and Migration Systems Theory (MST) to develop a model to characterize the structure and evolution of international migration flows. Methodologically, the Stochastic Actor-oriented Model of network dynamics is used to jointly model the three types of flows under analysis. Results show that endogenous network effects at the monadic, dyadic, and triadic levels of analysis are relevant to understand the emergence and evolution of migration flows. The findings also show that a core set of non-network covariates, suggested by MST as key drivers of migration flows, does not always explain migration dynamics in the systems under analysis in a consistent fashion; thus, suggesting the existence of important levels of heterogeneity inherent to these three types of flows. Finally, evidence related to the role of political instability and countries’ care deficits is also discussed as part of the analysis. Overall, the results highlight the importance of analyzing flows across the globe beyond typically studied migratory corridors (e.g., North–South flows) or regions (e.g., Europe).