One way to preserve a rare book is to lock it away from all potential sources of damage. Of course, an inaccessible book is also of little use, and the paper and ink will continue to degrade with age in any case. Like a book, the information stored in our DNA needs to be read, but it is also subject to continuous assault and therefore needs to be protected. In this Review, we examine how the replication stress response that is controlled by the kinase ataxia telangiectasia and Rad3-related (ATR) senses and resolves threats to DNA integrity so that the DNA remains available to read in all of our cells. We discuss the multiple data that have revealed an elegant yet increasingly complex mechanism of ATR activation. This involves a core set of components that recruit ATR to stressed replication forks, stimulate kinase activity and amplify ATR signalling. We focus on the activities of ATR in the control of cell cycle checkpoints, origin firing and replication fork stability, and on how proper regulation of these processes is crucial to ensure faithful duplication of a challenging genome.