Yes / Cracks in concrete composites, whether autogenous or loading-initiated, are almost inevitable and often difficult to detect and repair, posing a threat to safety and durability of concrete infrastructures, especially for those with strict sealing requirements. The sustainable development of infrastructures calls for the birth of self-healing concrete composites, which has the built-in ability to autonomously repair narrow cracks. This paper reviews the fabrication, characterization, mechanisms and performances of autogenous and autonomous healing concretes. Autogenous healing materials such as mineral admixtures, fibers, nanofillers and curing agents, as well as autonomous healing methods such as electrodeposition, shape memory alloys, capsules, vascular and microbial technologies, have been proven to be effective to partially or even fully repair small cracks. As a result, the mechanical properties and durability of concrete infrastructure can be restored to some extent. However, autonomous healing techniques have shown a better performance in healing cracks than most of autogenous healing methods that are limited to healing of cracks having a narrower width than 150 µm. Self-healing concrete with biomimetic features, such as self-healing concrete based on shape memory alloys, capsules, vascular networks or bacteria, is a frontier subject in the field of material science. Self-healing technology provides concrete infrastructures with the ability to adapt and respond to the environment, exhibiting a great potential to facilitate the creation of a wide variety of smart materials and intelligent structures.