Chatbots are conversational software applications designed to interact dialectically with users for a plethora of different purposes. Surprisingly, these colloquial agents have only recently been coupled with computational models of arguments (i.e. computational argumentation), whose aim is to formalise, in a machine-readable format, the ordinary exchange of information that characterises human communications. Chatbots may employ argumentation with different degrees and in a variety of manners. The present survey sifts through the literature to review papers concerning this kind of argumentation-based bot, drawing conclusions about the benefits and drawbacks that this approach entails in comparison with standard chatbots, while also envisaging possible future development and integration with the Transformer-based architecture and state-of-the-art Large Language models.