Tracking odour trails is a crucial behaviour for many animals, often leading to food, mates or away from danger. It is an excellent example of active sampling, where the animal itself controls how to sense the environment. Here we show that rats can track odour trails accurately with near-optimal sampling. We trained rats to follow odour trails drawn on paper spooled through a treadmill. By recording local field potentials (LFPs) from the olfactory bulb, and sniffing rates, we find that sniffing but not LFPs differ between tracking and non-tracking conditions. Rats can track odours within ~1 cm, and this accuracy is degraded when one nostril is closed. Moreover, they show path prediction on encountering a fork, wide 'casting' sweeps on encountering a gap and detection of reappearance of the trail in 1-2 sniffs. We suggest that rats use a multi-layered strategy, and achieve efficient sampling and high accuracy in this complex task.