Observation Data Used to Investigate Pigeon Homing -- Basic Features of Pigeon Homing -- Potential Input Signals Exploitable for Home-Finding -- The Role of the Sun -- The Role of the Geomagnetic Field -- The Role of the Chemical Atmosphere -- The Role of the Visual Landscape -- The Neural Bases of Pigeon Homing -- Homing in Other Birds -- Research History: Blind Alleys and an Unexpected Passage -- Overall Synthesis and Perspective. How migratory birds can navigate home from their wintering grounds to their breeding sites over hundreds and thousands of kilometres has been an admired mystery over more than a century. Profound advances towards a solution of this problem have been achieved with a model bird, the homing pigeon. This monograph summarizes our current knowledge about pigeon homing, about the birds' application of a sun compass and a magnetic compass, of a visual topographical map within a familiar area and -- most surprisingly -- of an olfactory map using atmospheric chemosignals as indicators of position in distant unfamiliar areas.