Currently about 11% of the world's energy is produced in nuclear power plants; this implies the processing of uranium in order to enrich it to be suitable for burning in a nuclear reactor. Besides other environmental and monetary costs involved in the whole nuclear fuel cycle, the enrichment process has the disadvantage of producing depleted uranium as a sub-product that has no wide use and is essentially stockpiled. One strategy to deal with this issue is to design a nuclear reactor that can run mostly on depleted uranium by breeding its own fissile fuel from it. Even though this concept could sound innovative or new, the truth is that it has been in the thought of the nuclear engineers since the 50s. In the present paper, the breed & burn (B&B) reactor concept is reviewed, as well as its origins, evolution up to present, and its main technical features. The objectives of this review are as follows: (1) to summarize the history of the development of B&B reactors, (2) to compare different B&B concepts based on a systematic approach under selected technical features, and (3) to bring out current trends and future directions on this technology. It is expected that this review will help the nuclear engineering community in general, and newcomer researchers in the field, to get an overview about the B&B reactors and how to direct a research in this direction.