Research at the Interaction Lab focuses on human-agent communication using conversational Natural Language. The ultimate goal is to create systems where humans and AI agents (including embodied robots) can spontaneously form teams and coordinate shared tasks through the use of Natural Language conversation as a universal communication interface. This paper first introduces machine learning approaches to problems in conversational AI in general, where computational agents must coordinate with humans to solve tasks using conversational Natural Language. It also covers some of the practical systems developed in the Interaction Lab, ranging from speech interfaces on smart speakers to embodied robots interacting using visually grounded language. In several cases communication between multiple agents is addressed. The paper surveys the central research problems addressed here, the approaches developed, and our main results. Some key open research questions and directions are then discussed, leading towards a future vision of conversational, collaborative multi-agent systems.