Biomimetic vision is a novel, interdisciplinary approach to machine vision. It is based on the observation that many natural organisms have evolved highly optimized visual strategies to control their behavior. These strategies are far superior to existing technical solutions, and can be used in a new generation of artificial systems to solve various control tasks. In this dissertation the author presents a complete, biomimetic vision system with a spherical field of view. He introduces various algorithms and data structures for the efficient acquisition, representation, processing and behavior-oriented evaluation of spherical images. The algorithms are inspired by the different processing stages in the visual system of flying insects, and are tested in the context of visual flight stabilization.