Living organisms are far superior to state-of-the-art robots as they have evolved a wide number of capabilities that far encompass our most advanced technologies. The merging of biological and artificial world, both physically and cognitively, represents a new trend in robotics that provides promising prospects to revolutionize the paradigms of conventional bio-inspired design as well as biological research. In this review, a comprehensive definition of animal-robot interactive technologies is given. They can be at animal level, by augmenting physical or mental capabilities through an integrated technology, or at group level, in which real animals interact with robotic conspecifics. Furthermore, an overview of the current state of the art and the recent trends in this novel context is provided. Bio-hybrid organisms represent a promising research area allowing us to understand how a biological apparatus (e.g. muscular and/or neural) works, thanks to the interaction with the integrated technologies. Furthermore, by using artificial agents, it is possible to shed light on social behaviours characterizing mixed societies. The robots can be used to manipulate groups of living organisms to understand self-organization and the evolution of cooperative behaviour and communication.