We estimate global inter-firm networks across all major industries from 1981 through 2016 and provide the first empirical tests for both robust (beneficial) and fragile (harmful) network behavior, relating firms' health with global integration. More connected firms are less likely to be in distress and have higher profit growth and equity returns, but are also more exposed to direct contagion from distressed neighboring firms and network level crises. Our analysis reveals the centrality of finance in the international firm network and increased globalization, with greater potential for crises to spread globally when they do occur.JEL codes: C3, F36, F61, G15