Computational persuasion aims to capture the human ability to persuade through argumentation for applications such as behaviour change in healthcare (e.g. persuading people to take more exercise or eat more healthily). In this paper, we review research in computational persuasion that incorporates domain modelling (capturing arguments and counterarguments that can appear in a persuasion dialogues), user modelling (capturing the beliefs and concerns of the persuadee), and dialogue strategies (choosing the best moves for the persuader to maximize the chances that the persuadee is persuaded). We discuss evaluation of prototype systems that get the user's counterarguments by allowing them to select them from a menu. Then we consider how this work might be enhanced by incorporating a natural language interface in the form of an argumentative chatbot.