Mimicking natural vascular systems in engineering materials is achievable by using core-shell nanofibers (NFs) whose cores are filled with self-healing agents (e.g., resin monomer and curing agent, or epoxy and hardener). This is beneficial for the following reasons: (i) uniformly distributed versus localized healing elements (as in the case of microcapsules containing healing agents), and (ii) nanoscale instead of microscale healing elements (as in the case of microcapsules). Nanoscale healing elements can fit ply areas in layered composites and avoid weakening the surrounding matrix. Another benefit of NF-based self-healing systems is that the dispersion of additional components required for self-healing reactions in the surrounding matrix is unnecessary. Specifically, a self-healing system should use two types of interwoven NFs with two complementary healing agents present within their cores, namely, a resin and its curing agent or an epoxy and its hardener. When released from the damaged core-shell nanofibers, these components react with each other to form polymerized, solidified stitches that connect the crack banks. The stiffness and self-cohesion of the damaged material can thus be restored. However, the prevention of delamination and the recovery of adhesion to surfaces of different compositions remain issues to be resolved that require additional future research efforts.