Language models, powered by recent revolutions in AI, are becoming increasingly more powerful and support language generation, summarization, classification, question answering, chatbots and more. In this research project, we aim to create dialogue systems that simulate human dialogue in a social context, allowing human-machine communication to be more effective and enjoyable for humans. This work will capitalize on recent developments in LSTM and Transformer models, on the one hand, and on recent advances in computational construction grammar on the other, to build applications which focus on language and linguistic interaction. One of the envisioned application domains is education support, which ranges from the generation of questions or multiple choice distractors from educational text, to interactive learning with and explanation by embodied agents. We will thus also explore multimodal interaction, in which language is combined with other modalities, such as vision.