This paper considers the problem of how to display visual space naturalistically in image media. A long-standing solution is linear perspective projection, which is currently used in imaging technologies from cameras to 3D graphics renderers. Linear perspective has many strengths but also some significant weaknesses and over the centuries alternative techniques have been developed for creating more naturalistic images. Here we discuss the problem, its scientific background, and some of the approaches taken by artists and computer graphics researchers to find solutions. We briefly introduce our own approach, which is a form of nonlinear 3D geometry modelled on the perceptual structure of visual space and designed to work on standard displays. We conclude that perceptually modelled nonlinear approaches can make 3D imaging technology more naturalistic than methods based on linear perspective.