Structural polymer composites are susceptible to premature failure in the form of microcracks in the matrix. Although benign initially when they form, these matrix cracks tend to coalesce and lead in service to critical damage modes such as ply delamination. The matrix cracks are difficult to detect and almost impossible to repair because they form inside the composite laminate. Therefore, polymers with self-healing capability would provide a promising potential to minimize maintenance costs while extending the service lifetime of composite structures. In this paper we report on a group of polymers and their composites which exhibit mendable property upon heating. The failure and healing mechanisms of the polymers involve Diels-Alder (DA) and retro-Diels-Alder (RDA) reactions on the polymer back-bone chain, which are thermally reversible reactions requiring no catalyst. The polymers exhibited good healing property in bulk form. Composite panels were prepared by sandwiching the monomers between carbon fiber fabric layers and cured in autoclave. Microcracks were induced on the resin-rich surface of composite with Instron machine at room temperature by holding at 1% strain for 1 min. The healing ability of the composite was also demonstrated by the disappearance of microcracks after heating. In addition to the self-healing ability, the polymers and composites also exhibited shape memory property. These unique properties may provide the material multi-functional applications. Resistance heating of traditional composites and its applicability in self-healing composites is also studied to lay groundwork for a fully integrated self-healing composite.