We use language to communicate our thoughts. But is language merely the expression of thoughts, which are themselves produced by other, nonlinguistic parts of our minds? Or does language play a more transformative role in human cognition, allowing us to have thoughts that we otherwise could (or would) not have? Recent developments in artificial intelligence (AI) and cognitive science have reinvigorated this old question. We argue that language may hold the key to the emergence of both more general AI systems and central aspects of human intelligence. We highlight two related properties of language that make it such a powerful tool for developing domain--general abilities. First, language offers compact representations that make it easier to represent and reason about many abstract concepts (e.g., exact numerosity). Second, these compressed representations are the iterated output of collective minds. In learning a language, we learn a treasure trove of culturally evolved abstractions. Taken together, these properties mean that a sufficiently powerful learning system exposed to language--whether biological or artificial--learns a compressed model of the world, reverse engineering many of the conceptual and causal structures that support human (and human-like) thought.