Recent breakthroughs in artificial intelligence (AI) have enabled machines to plan in tasks previously thought to be uniquely human. Meanwhile, the planning algorithms implemented by the brain itself remain largely unknown. Here, we review neural and behavioral data in sequential decision-making tasks that elucidate the ways in which the brain does-and does not-plan. To systematically review available biological data, we create a taxonomy of planning algorithms by summarizing the relevant design choices for such algorithms in AI. Across species, recording techniques, and task paradigms, we find converging evidence that the brain represents future states consistent with a class of planning algorithms within our taxonomy-focused, depth-limited, and serial. However, we argue that current data are insufficient for addressing more detailed algorithmic questions. We propose a new approach leveraging AI advances to drive experiments that can adjudicate between competing candidate algorithms.