This paper introduces Sentient Embodied Conversational Agents (SECAs) as virtual characters able to engage users in complex conversations. Our proposal includes the formalisation of a SECA architecture together with a software library that facilitates their inclusion in applications requiring proactive and sensitive agent behaviours. Since educational and eldercare applications constitute paradigmatic examples of such requirements, we evaluate our proposal with a virtual tutor embedded in an educational application. The obtained results show that children are satisfied both in terms of their perception of learning and overall conversational experience. Additionally, we found significant differences in quantity of user data gathered by our application (with SECA) and its previous version (without SECA).