This book gives an overview of the existing self-healing nanotextured vascular approaches. Itdescribes the healing agents used in engineering self-healing materials as well as thefundamental physicochemical phenomena accompanying self-healing. This book also addressesthe different fabrication methods used to form core-shell nanofiber mats. The fundamentaltheoretical aspects of fracture mechanics are outlined. A brief theoretical description of cracksin brittle elastic materials is given and the Griffith approach is introduced. The fracturetoughness is described, including viscoelastic effects. Critical (catastrophic) and subcritical(fatigue) cracks and their growth are also described theoretically. The adhesion and cohesionenergies are introduced as well, and the theory of the blister test for the two limiting cases ofstiff and soft materials is developed. In addition, the effect of non-self-healing nanofiber matson the toughening of ply surfaces in composites is discussed. The book also presents a briefdescription of the electrochemical theory of corrosion crack growth. All the above-mentionedphenomena are relevant in the context of self-healing materials.