The polypterids (bichirs and ropefish) are extant basal actinopterygian (ray-finned) fishes that breathe air and share similarities with extant lobe-finned sarcopterygians (lungfishes and tetrapods) in lung structure. They are also similar to some fossil sarcopterygians, including stem tetrapods, in having large paired openings (spiracles) on top of their head. The role of spiracles in polypterid respiration has been unclear, with early reports suggesting that polypterids could inhale air through the spiracles, while later reports have largely dismissed such observations. Here we resolve the 100-year-old mystery by presenting structural, behavioural, video, kinematic and pressure data that show spiracle-mediated aspiration accounts for up to 93% of all air breaths in four species of Polypterus. Similarity in the size and position of polypterid spiracles with those of some stem tetrapods suggests that spiracular air breathing may have been an important respiratory strategy during the fish-tetrapod transition from water to land.