Exactly half a century has passed since the launch of the first documented research project (1965 Dendral) on computer-assisted organic synthesis. Many more programs were created in the 1970s and 1980s but the enthusiasm of these pioneering days had largely dissipated by the 2000s, and the challenge of teaching the computer how to plan organic syntheses earned itself the reputation of a "mission impossible". This is quite curious given that, in the meantime, computers have "learned" many other skills that had been considered exclusive domains of human intellect and creativity-for example, machines can nowadays play chess better than human world champions and they can compose classical music pleasant to the human ear. Although there have been no similar feats in organic synthesis, this Review argues that to concede defeat would be premature. Indeed, bringing together the combination of modern computational power and algorithms from graph/network theory, chemical rules (with full stereo- and regiochemistry) coded in appropriate formats, and the elements of quantum mechanics, the machine can finally be "taught" how to plan syntheses of non-trivial organic molecules in a matter of seconds to minutes. The Review begins with an overview of some basic theoretical concepts essential for the big-data analysis of chemical syntheses. It progresses to the problem of optimizing pathways involving known reactions. It culminates with discussion of algorithms that allow for a completely de novo and fully automated design of syntheses leading to relatively complex targets, including those that have not been made before. Of course, there are still things to be improved, but computers are finally becoming relevant and helpful to the practice of organic-synthetic planning. Paraphrasing Churchill's famous words after the Allies' first major victory over the Axis forces in Africa, it is not the end, it is not even the beginning of the end, but it is the end of the beginning for the computer-assisted synthesis planning. The machine is here to stay.