Microbially induced calcium carbonate precipitation (MICP) has been widely explored and applied in the field of environmental engineering over the last decade. Calcium carbonate is naturally precipitated as a byproduct of various microbial metabolic activities. This biological process was brought into practical use to restore construction materials, strengthen and remediate soil, and sequester carbon. MICP has also been extensively examined for applications in self-healing concrete. Biogenic crack repair helps mitigate the high maintenance costs of concrete in an eco-friendly manner. In this process, calcium carbonate precipitation (CCP)-capable bacteria and nutrients are embedded inside the concrete. These bacteria are expected to increase the durability of the concrete by precipitating calcium carbonate in situ to heal cracks that develop in the concrete. However, several challenges exist with respect to embedding such bacteria; harsh conditions in concrete matrices are unsuitable for bacterial life, including high alkalinity (pH up to 13), high temperatures during manufacturing processes, and limited oxygen supply. Additionally, many biological factors, including the optimum conditions for MICP, the molecular mechanisms involved in MICP, the specific microorganisms suitable for application in concrete, the survival characteristics of the microorganisms embedded in concrete, and the amount of MICP in concrete, remain unclear. In this paper, metabolic pathways that result in conditions favorable for calcium carbonate precipitation, current and potential applications in concrete, and the remaining biological challenges are reviewed.