Building socially-intelligent AI agents (Social-AI) is a multidisciplinary, multimodal research goal that involves creating agents that can sense, perceive, reason about, learn from, and respond to affect, behavior, and cognition of other agents (human or artificial). Progress towards Social-AI has accelerated in the past decade across several computing communities, including natural language processing, machine learning, robotics, human-machine interaction, computer vision, and speech. Natural language processing, in particular, has been prominent in Social-AI research, as language plays a key role in constructing the social world. In this position paper, we identify a set of underlying technical challenges and open questions for researchers across computing communities to advance Social-AI. We anchor our discussion in the context of social intelligence concepts and prior progress in Social-AI research.