This review summarizes research on peripheral vision and its relation to theories of form perception. After a historical overview, it describes quantifications of the cortical magnification hypothesis, including an extension of Schwartz's cortical mapping function. The merits of this concept are considered across a wide range of psychophysical tasks, followed by a discussion of its limitations and the need for non-spatial scaling. It also reviews the eccentricity dependence of other low-level functions including reaction time, temporal resolution and spatial summation, as well as perimetric methods. A central topic is the recognition of characters in peripheral vision, both at low and high levels of contrast, and the impact of surrounding contours known as crowding. It demonstrates how Bouma's law, specifying the critical distance for the onset of crowding, can be stated in terms of the retino-cortical mapping. The recognition of more complex stimuli, like textures, faces and scenes reveals a substantial impact of mid-level vision and cognitive factors. It further considers eccentricity-dependent limitations of learning, both at the level of perceptual learning and pattern category learning. Generic limitations of extrafoveal vision are observed for the latter in categorization tasks involving multiple stimulus classes. Finally, models of peripheral form vision are discussed. It reports that peripheral vision is limited with regard to pattern categorization by a distinctly lower representational complexity and processing speed. Taken together, the limitations of cognitive processing in peripheral vision appear to be as significant as those imposed on low-level functions and by way of crowding.This review summarizes research on peripheral vision and its relation to theories of form perception. After a historical overview, it describes quantifications of the cortical magnification hypothesis, including an extension of Schwartz's cortical mapping function. The merits of this concept are considered across a wide range of psychophysical tasks, followed by a discussion of its limitations and the need for non-spatial scaling. It also reviews the eccentricity dependence of other low-level functions including reaction time, temporal resolution and spatial summation, as well as perimetric methods. A central topic is the recognition of characters in peripheral vision, both at low and high levels of contrast, and the impact of surrounding contours known as crowding. It demonstrates how Bouma's law, specifying the critical distance for the onset of crowding, can be stated in terms of the retino-cortical mapping. The recognition of more complex stimuli, like textures, faces and scenes reveals a substantial impact of mid-level vision and cognitive factors. It further considers eccentricity-dependent limitations of learning, both at the level of perceptual learning and pattern category learning. Generic limitations of extrafoveal vision are observed for the latter in categorization tasks involving multiple stimulus classes. Finally, models of peripheral form vision are discussed. It reports that peripheral vision is limited with regard to pattern categorization by a distinctly lower representational complexity and processing speed. Taken together, the limitations of cognitive processing in peripheral vision appear to be as significant as those imposed on low-level functions and by way of crowding.