Magic lenses are popular tools to provide locally altered views of visual data. In this paper, we introduce the concept of BodyLenses, special kinds of magic lenses for wall displays that are mainly controlled by body interactions. After motivating the rationale for body-centric lenses, we present a comprehensive design space of BodyLenses, where we analyse fundamental aspects such as appearance, function, interaction and use in multi-user contexts. Within that space, we investigated and implemented a number of design alternatives and propose solutions for lens positioning, dynamic shape modification, distance-based parameter mappings and the use of BodyLenses as portable tool belts. We demonstrate the practicality of our novel concepts with four realised application scenarios. With this work, we hope to lay the foundation for future research and systems based on body-driven lenses.