Cementand concrete are vital materials used to construct durablehabitats and infrastructure that withstand natural and human-causeddisasters. Still, concrete cracking imposes enormous repair costson societies, and excessive cement consumption for repairs contributesto climate change. Therefore, the need for more durable cementitiousmaterials, such as those with self-healing capabilities, has becomemore urgent. In this review, we present the functioning mechanismsof five different strategies for implementing self-healing capabilityinto cement based materials: (1) autogenous self-healing from ordinaryportland cement and supplementary cementitious materials and geopolymersin which defects and cracks are repaired through intrinsic carbonationand crystallization; (2) autonomous self-healing by (a) biomineralizationwherein bacteria within the cement produce carbonates, silicates,or phosphates to heal damage, (b) polymer-cement compositesin which autonomous self-healing occurs both within the polymer andat the polymer-cement interface, and (c) fibers that inhibitcrack propagation, thus allowing autogenous healing mechanisms tobe more effective. In all cases, we discuss the self-healing agentand synthesize the state of knowledge on the self-healing mechanism(s).In this review article, the state of computational modeling acrossnano- to macroscales developed based on experimental data is presentedfor each self-healing approach. We conclude the review by noting that,although autogenous reactions help repair small cracks, the most fruitfulopportunities lay within design strategies for additional componentsthat can migrate into cracks and initiate chemistries that retardcrack propagation and generate repair of the cement matrix.