What kinds of hidden shapes lie in natural images, and what can they tell us about how neural networks learn? It turns out small patches of natural images are not arranged randomly, but around unexpected geometric structures such as circles and the Klein bottle. Later works found closely related topological organization in the learned spatial filters of convolutional neural networks (CNN). This leads to a new kind of architecture, called the Topological CNN, that builds this topology into the architecture of the neural network. TCNN outperforming the traditional CNN in various tasks suggests that learning can be strengthened by exploiting the topology and latent structure of data itself.