Embryonic tissues heal wounds rapidly and without scarring, in a process conserved across species and driven by collective cell movements. The mechanisms of coordinated cell movement during embryonic wound closure also drive tissue development and cancer metastasis; therefore, embryonic wound repair has received considerable attention as a model of collective cell migration. During wound closure, a supracellular actomyosin cable at the wound edge coordinates cells, while actin-based protrusions contribute to cell crawling and seamless wound healing. Other cytoskeletal networks are reorganized during wound repair: microtubules extend into protrusions and along cell-cell boundaries as cells stretch into damaged regions, septins accumulate at the wound margin, and intermediate filaments become polarized in the cells adjacent to the wound. Thus, diverse cytoskeletal networks work in concert to maintain tissue structure, while also driving and organizing cell movements to promote rapid repair. Understanding the signals that coordinate the dynamics of different cytoskeletal networks, and how adhesions between cells or with the extracellular matrix integrate forces across cells, will be important to elucidate the mechanisms of efficient embryonic wound healing and may have far-reaching implications for developmental and cancer cell biology.