Surround perception is crucial for an immersive sense of presence in communication and for efficient navigation and surveillance in robotics. To enable surround perception, new omnidirectional systems were designed, which gave a new impetus for rethinking the way images, are acquired and analyzed. Based on insights gained from such designs, we formulate a novel unifying theory of imaging. We prove that all single viewpoint mirror-lens devices are equivalent to projective mappings from the sphere to the plane. These mappings are paired with a duality principle, which relates points to line projections. The commonly used parabolic mirror projection is shown to be equivalent to the stereographic projection, providing therefore the invariants of a conformal mapping. It turns out that conventional cam-eras, which are only a special case in our theory, provide the barest minimum of information about the environment. We review current approaches to omnidirectional imaging and present a framework for calibration of omnidirectional cameras from single views.