Natural images have been shown to exhibit predictable statistical properties, including consistent pairwise luminance statistics, spatiotemporal statistics, and contrast and intensity distributions. Since evolution has presumably selected neural coding strategies that are highly efficient with respect to representational, metabolic and developmental resources, statistical regularities can be used to predict why visual systems show the visual coding strategies they do. This dissertation begins with a new theoretical foundation of efficient visual coding and it describes a suite of studies aimed at testing and expanding specific hypotheses of efficient coding of natural images. It is specifically concerned with applying notions of coding efficiency deduced from statistical regularities of natural scenes to images created for human viewing, especially artworks. From the perspective of visual coding, paintings are a rich and largely unexplored class of images. As will be shown, the fact that paintings (even highly abstract ones) share the same basic statistical redundancies as natural scenes suggests that humans exploit efficient coding strategies used by the brain in order to make two dimensional representations that can be viewed by the eye. The findings presented in Chapter 2, which show a model of how retinal processing can be matched to regularities in the spatial frequency power spectrum of scenes, are especially relevant to art. I argue that because evolution appears to have chosen retinal coding schemes that are efficient with respect to statistical regularity in natural scenes, art whose statistics deviate strongly from such regularity will be attempted rarely. The proposals regarding coding efficiency are employed to explain why art through the ages shows the statistical regularity it does. This ?perceptibility hypothesis? argues against explanations for art?s statistical regularity that invoke universal aesthetics. However, artists must fundamentally alter some statistical properties of scenes in order to depict them in paint. A statistical model of how artists compress the large dynamic range of luminances in scenes into the far smaller range available in paint is also presented. I show that no single functional form can describe artists? nonlinear luminance compression strategies, and I propose that each painter?s compression strategy may be characteristic to her work.