The sensory and perceptual capabilities of biological organisms are still well beyond what we have been able to emulate with machines, and the brain devotes far more neural resources to the problems of sensory coding and early perception than we give credit in our algorithms. What is it all doing? Although a great deal has been learned about anatomical structure and physiological properties, insights into the underlying information processing algorithms have been difficult to obtain. Recent work, however, that has begun to elucidate some of the underlying computational principles and processes that biology uses to transform the raw sensory signal into a hierarchy of representations that subserve higher-level perceptual tasks. A central hypothesis in this work is that biological representations are optimal from the viewpoint of statistical information processing, and adapt to the statistics of the natural sensory environment. In this tutorial, I will review work on learning sensory codes that are optimal for the statistics of the natural sensory environment and show how these results provide theoretical explanations for a variety of physiological data in both the auditory and visual systems. This will include work that that has extended these results to provide functional explanations for many non-linear aspects of early auditory and visual processing. I will focus on work on the auditory and visual systems but also emphasize the generality of these approaches and how they can be applied to any sensory domain. I will also discuss work that generalizes the basic theory and shows how neural representations optimally compensate for sensory distortion and noise in neural populations. Finally, I will review work that goes beyond sensory coding and investigates the computational problems involved in computing more abstract sensory properties and invariant features that can subserve higher-level tasks such as perceptual organization and analysis of complex, natural scenes.