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17 USC 105 interim-entered record; under review. The article of record as published may be found at https://doi.org/10.1002/net.21996 Fifty years of research in Networks coincides with 50 years of advances in resilience theory and applications. The purpose of this review is to identify how these two technical communities influenced each other in the past and can bolster each other in the future. Advances in resilience theory show that there are at least four ways networks demonstrate resilience: robustness, rebound, extensibility, and adaptability. Research published in Networks and by the broader network optimization community has focused primarily on technical methods for robustness and rebound. We review this literature to organize seminal problems and papers on the ability of networks to manage increasing stressors and return to normal activities after a stressful event. In contrast, the Networks community has made less progress addressing issues for network extensibility and adaptability. Extensibility refers to the ability to stretch current operations to surprising situations and adaptability refers to the ability to sustain operations into the future. We discuss ways to harness existing network optimization methods to study these forms of resilience and outline their limitations. We conclude by providing a research agenda that ensures the Networks community remains central to future advances in resilience while being pragmatic about the limitations of network optimization for achieving this task. This research was supported by the Defense Threat Reduction Agency, Grant/Award Number: DTRA-18681-M. National Science Foundation, Grant/Award Number: CMMI-1254258.