The visual system is the most studied sensory pathway, which is partly because visual stimuli have rather intuitive properties. There are reasons to think that the underlying principle ruling coding, however, is the same for vision and any other type of sensory signal, namely the code has to satisfy some notion of optimality--understood as minimum redundancy or as maximum transmitted information. Given the huge variability of natural stimuli, it would seem that attaining an optimal code is almost impossible; however, regularities and symmetries in the stimuli can be used to simplify the task: symmetries allow predicting one part of a stimulus from another, that is, they imply a structured type of redundancy. Optimal coding can only be achieved once the intrinsic symmetries of natural scenes are understood and used to the best performance of the neural encoder. In this paper, we review the concepts of optimal coding and discuss the known redundancies and symmetries that visual scenes have. We discuss in depth the only approach which implements the three of them known so far: translational invariance, scale invariance and multiscaling. Not surprisingly, the resulting code possesses features observed in real visual systems in mammals.