The work of archaeozoologists and molecular geneticists suggests that the domestication of the wolf (Canis lupus)—the ancestor of the domestic dog (C. familiaris)—probably occurred somewhere between 40,000 and 15,000 years ago somewhere on the Eurasian continent, perhaps in more than one location. Wolf domestication was therefore underway many millennia before the origins of agriculture and the domestication of food animals, such as sheep and goats. Currently, there are two predominant “origin stories” concerning the domestication of the wolf. The dominant narrative in recent literature is the commensal scavenger hypothesis which posits that wolves essentially domesticated themselves by invading ancient human settlements in search of animal remains and other edible waste discarded by hunter-gatherers. Over time, tolerance by humans gave a selective advantage to the bolder, less fearful wolves, which then diverged from the ancestral population as they adapted to the new scavenging niche. At some point in the process, humans also began to recognize the benefits of living with resident, semi-domestic wolves, either as guards or as hunting partners, thereby cementing the relationship. The alternative account of wolf domestication is very different. Sometimes known as the pet keeping or cross-species adoption hypothesis, this narrative draws heavily on anthropological observations of pet keeping among recent hunter-gatherers, and postulates that Paleolithic peoples were similarly inclined to capture, adopt and rear infant mammals, such as wolf pups, and that this habitual human nurturing behavior ultimately provided the basis for the evolution of a cooperative social system involving both species. This review critically examines and analyzes these two distinct domestication narratives and explores the underlying and sometimes erroneous assumptions they make about wolves, Pleistocene humans, and the original relationships that existed between the two species. The paper concludes that the commensal scavenger hypothesis is untenable based on what is known about recent and ancient hunter-gatherer societies, and that wolf domestication was predicated on the establishment of cooperative social relations between humans and wolves based on the early socialization of wolf pups.