Large language models (LLMs) are transforming human-computer interaction and conceptions of artificial intelligence (AI) with their impressive capacities for conversing and reasoning in natural language. There is growing interest in whether LLMs have theory of mind (ToM); the ability to reason about the mental and emotional states of others that is core to human social intelligence. As LLMs are integrated into the fabric of our personal, professional and social lives and given greater agency to make decisions with real-world consequences, there is a critical need to understand how they can be aligned with human values. ToM seems to be a promising direction of inquiry in this regard. Following the literature on the role and impacts of human ToM, this paper identifies key areas in which LLM ToM will show up in human:LLM interactions at individual and group levels, and what opportunities and risks for alignment are raised in each. On the individual level, the paper considers how LLM ToM might manifest in goal specification, conversational adaptation, empathy and anthropomorphism. On the group level, it considers how LLM ToM might facilitate collective alignment, cooperation or competition, and moral judgement-making. The paper lays out a broad spectrum of potential implications and suggests the most pressing areas for future research.