Embodied conversational agents are capable of carrying a face-to-face interaction with users. Their use is substantially increasing in numerous applications ranging from tutoring systems to ambient assisted living. In such applications, one of the main challenges is to keep the user engaged in the interaction with the agent. The present chapter provides an overview of the scientic issues underlying the engagement paradigm, including a review on methodologies for assessing user engage- ment in human-agent interaction. It presents three studies that have been conducted within the Greta/VIB platforms. These studies aimed at designing engaging agents using dierent interaction strategies (alignment and dynamical coupling) and the expression of interpersonal attitudes in multi-party interactions.