Self-healing composites are composite materials capable of automatic recovery when damaged. They are inspired by biological systems such as the human skin which are naturally able to heal themselves. This paper reviews work on self-healing composites with a focus on capsule-based and vascular healing systems. Complementing previous survey articles, the paper provides an updated overview of the various self-healing concepts proposed over the past 15 years, and a comparative analysis of healing mechanisms and fabrication techniques for building capsules and vascular networks. Based on the analysis, factors that influence healing performance are presented to reveal key barriers and potential research directions.