Animal domestication is considered a complex and multistage process that altered behaviorally, morphologically, and physiologically the domesticates relative to their wild ancestors. Ever since Darwin, scientists have been concerned about the history of domestication. To determine the domestication origins of the species, it is crucial to discover their ancestors and identify the approximate local domestication. Domestication has been the focus of several studies from different specialties. Studying when, where, and how domestication happened is essential to understand the origins of civilizations and the evolution of domesticated species. The development of both humans and domestic animals is hard to justify, and the genetic variations that occurred during the early animal domestication process remain vague. The recent and potential applications of evolutionary biology may deliver answers for main social challenges. It is important to examine the relationship among the environment and the traits of organisms that have been influenced through the adaptation to modern environments and the patterns of selection triggered by their environments during domestication period. Once domestication occurred, several events such as gene flow and selective pressures occurred, leading to genomic and phenotypic alterations. In this review, we discuss the current knowledge about the spatiotemporal outlines of domestication and debates surrounding the intent, speed, and evolutionary landscapes of this event. We also focus on the core challenges for future research. In conclusion, we argue that although the current growth in domestication information …