We propose detailed classifications of different calibration methods for catadioptric systems and a novel non-central catadioptric sensor autocalibration approach. The first part provides most calibration approaches found in literature classified based on basic common criteria between these methods and widely used assumptions employed by them. Currently there is no such detailed classification considering all these criteria and assumptions together. We cover both central and non-central catadioptric systems and show how frequently certain assumptions are taken in order to calibrate different catadioptric systems. The classified techniques provide an important review for the vision and robotics community at large. The second part proposes a novel non-central catadioptric sensor auto-calibration approach. It uses polarization imaging and catacaustics. Our novel approach helps to auto-calibrate any combination of specular surfaces and lenses.