Although most works in computer vision use perspective or other central cameras, the interest in non-central camera models has increased lately, especially with respect to omnidirectional vision. Calibration and structure-from-motion algorithms exist for both, central and non-central cameras. An intermediate class of cameras, although encountered rather frequently, has received less attention. So-called axial cameras are non-central but their projection rays are constrained by the existence of a line that cuts all of them. This is the case for stereo systems, many non-central catadioptric cameras and pushbroom cameras for example. In this paper, we study the geometry of axial cameras and propose a calibration approach for them. We also describe the various axial catadioptric configurations which are more common and less restrictive than central catadioptric ones. Finally we used simulations and real experiments to prove the validity of our theory.