Many birds are able to find their previously established home site after passive displacement to distant localities far from any familiar landmarks. It is evident that they determine their position relative to home neither by path integration nor by deducing it from location-specific solar, stellar, magnetic or infrasonic signals. They need, however, unobstructed olfactory contact with the local atmosphere, and they must have experienced natural winds at the home site over at least several weeks. Further, they require the sun or the geomagnetic field as a directional compass reference. The empirical findings proving and characterizing olfactory navigation by birds (mainly homing pigeons) have been reported elsewhere and are briefly itemized here. It is further shown that trace gases are dispersed in the ground-level atmosphere with some regularity, including differently oriented gradients of ratios among certain hydrocarbons. A preliminary navigation model is based on such long-range ratio gradients and on their relation to wind direction. Within a familiar area around home, pigeons rely not only on olfactory inputs but also on the visual landscape for home-finding. The olfaction-based mechanism has been linked to the piriform cortex, the vision-based mechanism to the hippocampal formation. Adequacy of the term 'map' is discussed with respect to either mechanism. Remaining gaps in our knowledge and challenges for future research are addressed.