Trap–Neuter–Return and its variants (hereafter TNR) aims to control unowned cat populations. Papers on this topic form a useful case study of how how an area of literature grows, papers become influential, and citation networks form, influencing future study as well as public perceptions of the science. We analysed 145 TNR studies published 2002–2019. Common topics, identified by frequently used language, were population control, interactions with wildlife, disease transmission (including implications for pets, wildlife and humans), free-roaming cats, and feral and domestic cat management. One or more papers on each of these topics was judged influential because of high citations overall, high average citations/year, or frequent mentions in social media. Open Access papers were more influential in social media, raising greater public awareness than studies published in journals that were less accessible. While divergent views exist on a range of topics, the network analysis of the TNR literature indicated potential for forming self-reinforcing groups of authors. While it is encouraging that diverse views are expressed, there is a risk of reduced dialogue interactions between groups, potentially constraining dialogue to refine arguments, share information, or plan research. Journal editors could encourage communication by choosing reviewers from different camps to assess manuscripts and by asking authors to acknowledge alternative views.