The study of human-animal interactions (HAI), and the resulting human-animal relationships (HARs) and bonds (HABs) which are set up as a consequence, is currently a topical issue in comparative psychology. Here we review the HAI/HAR/HAB literature to detect the main publication trends, and to identify the predominant research themes in this area. Research in HAI/HAR/HAB only really started in the 1980s, but since then there has been a growth in studies which is still continuing. Most of these studies have been in the contexts of companion animal or agricultural animal research, but there is now a growing literature on laboratory, zoo and wild animals too. In the companion animal HAI/HAB literature the greatest emphasis has been on Animal-assisted Interventions (AAI), and the benefits to people of pet ownership and interaction with pets. Agricultural HAI/HAR research, on the contrary, has been more concerned with the welfare consequences of HAI/HARs to the animals. This disjunction is reflected in the preference of companion animal researchers to use the term ‘bond’, but agricultural researchers to use ‘relationship’. Other themes prominent in the literature include methodological issues, the characteristics of caretakers, the role of veterinarians, sociological approaches, and theoretical aspects. It is concluded that currently HAI/HAR/HAB research does not constitute a unified field, and there is a need to: i) agree and define a standard terminology; ii) undertake more research on the effects of HAI on companion animals; iii) undertake more research on the form and frequency of interactions; and iv) increase research on HAI/HAR/HABs in laboratory, zoo and wild-living animals. This research is important to understand whether HAI has positive, neutral or negative consequences, both for humans and for animals.