Challenging studies of engineered self-healing and self-repairing functions in concrete structures are briefly reviewed. While self-healing of concrete has been studied for a long time, it was only recently noticed that some engineered technologies are useful to stimulate the potential of concrete to be self-healed. For example, fiber reinforced cementitious composites (FRCC) have a much higher potential of self-healing than ordinary concrete because of their capability to keep cracks thinner and also because of the bridging network system in cracks; a specific bio-chemical approach, i.e. the application of mineral-precipitating bacteria, is now available; and various mineral admixtures are useful for practical application. Furthermore, the new concept of self-repairing concrete, which is based on the design concept of intelligent materials, is reported. Self-repairing concrete is concrete that incorporates devices for achieving the three key functions of an intelligent material, (1) sensing, (2) processing, and (3) actuating. This paper is a state-of-the-art report on the recent development of engineered self-healing and self-repairing concrete.