n the last decades it became clear that the living systems represent the new frontiers of the “exact sciences”. Mathematics and physics on one side, and biology on the other, are more and more interconnecting and taking mutual advantage from this interplay. In this talk I will discuss mathematical and computational neuroscience, by focusing on the case of the visual system and pointing out different approaches to its study. In particular, in the second part of the talk, I will discuss more specifically some recent results on functional maps in the visual cortex of higher mammals, from both the experimental and the theoretical point of view.