Crates of Mallos, a Hellenistic grammarian and geographer, is known to have combined Homeric exegesis and mathematical geography into a comprehensive world-view. His views appear to have influenced a tradition of map-making, as evidenced by an unusual late antique map that locates parts of Odysseus’s voyage from Aeaea to Hades according to Crates’ geography. This essay elucidates Crates’ geographical accounts of the Homeric Laestrygonians and of the constellation Draco and his understanding of the arctic circle in light of the map and of earlier geographers, particularly Pytheas of Massalia, who similarly incorporated Homeric references into his theorizing about the fixed arctic circle.