The environments we live in and the tasks we perform in those environments have shaped the design of our visual systems through evolution and experience. This is an obvious statement, but it implies three fundamental components of research we must have if we are going to gain a deep understanding of biological vision systems: (a) a rigorous science devoted to understanding natural environments and tasks, (b) mathematical and computational analysis of how to use such knowledge of the environment to perform natural tasks, and (c) experiments that allow rigorous measurement of behavioral and neural responses, either in natural tasks or in artificial tasks that capture the essence of natural tasks. This approach is illustrated with two example studies that combine measurements of natural scene statistics, derivation of Bayesian ideal observers that exploit those statistics, and psychophysical experiments that compare human and ideal performance in naturalistic tasks.