Fanconi anemia is a genetically heterogeneous disorder associated with chromosome instability and a highly elevated risk for developing cancer. The mutated genes encode proteins involved in the cellular response to DNA replication stress. Fanconi anemia proteins are extensively connected with DNA caretaker proteins, and appear to function as a hub for the coordination of DNA repair with DNA replication and cell cycle progression. At a molecular level, however, the raison d'être of Fanconi anemia proteins still remains largely elusive. The thirteen Fanconi anemia proteins identified to date have not been embraced into a single and defined biological process. To help put the Fanconi anemia puzzle into perspective, we begin this review with a summary of the strategies employed by prokaryotes and eukaryotes to tolerate obstacles to the progression of replication forks. We then summarize what we know about Fanconi anemia with an emphasis on biochemical aspects, and discuss how the Fanconi anemia network, a late acquisition in evolution, may function to permit the faithful and complete duplication of our very large vertebrate chromosomes.