How human language evolved remains one of the most intriguing questions in science, and different approaches have been used to tackle this question. A recent hypothesis, the Interaction Engine Hypothesis, postulates that language was made possible through the special capacity for social interaction involving different social cognitive skills (e.g., joint attention, common ground) and specific characteristics such as face-to-face interaction, mutual gaze and turn-taking, the exchange of rapid communicative turns. Recently, it has been argued that this turn-taking infrastructure may be a foundational and ancient mechanism of the layered system of language because communicative turn-taking has been found in human infants and across several non-human primate species. Moreover, there is some evidence for turn-taking in different mammalian taxa, especially those capable of vocal learning. Surprisingly, however, the existing studies have mainly focused on turn-taking production of adult individuals, while little is known about its emergence and development in young individuals. Hence, the aim of the current paper was 2-fold: First, we carried out a systematic review of turn-taking development and acquisition in mammals to evaluate possible research bias and existing gaps. Second, we highlight research avenues to spur more research into this domain and investigate if distinct turn-taking elements can be found in other non-human animal species. Since mammals exhibit an extended development period, including learning and strong parental care, they represent an excellent model group in which to investigate the acquisition and development of turn-taking abilities. We performed a systematic review including a wide range of terms and found 21 studies presenting findings on turn-taking abilities in infants and juveniles. Most of these studies were from the last decade, showing an increased interest in this field over the years. Overall, we found a considerable variation in the terminologies and methodological approaches used. In addition, studies investigating turn-taking abilities across different development periods and in relation to different social partners were very rare, thereby hampering direct, systematic comparisons within and across species. Nonetheless, the results of some studies suggested that specific turn-taking elements are innate, while others are acquired during development (e.g., flexibility). Finally, we pinpoint fruitful research avenues and hypotheses to move the field of turn-taking development forward and improve our understanding of the impact of turn-taking on language evolution.