The surface of the human brain is highly convoluted with many folds and fissures that vary in size, shape and location from person to person. Functional brain activity also occurs on the cortical surface and variability in surface shape makes it difficult to compare brains and identify regions which are related to a particular function. The cortical brain surface (corresponding to grey matter) is topologically equivalent to a two-dimensional sheet. There is great interest in unfolding or flattening the surface of the brain in order to create a 2D flat map of the cortex to assist in mapping brain function. In this presentation, I will discuss some of the topological difficulties encountered while trying to obtain a surface representation of the brain from high-resolution 3D magnetic resonance (MRI) images. I will show some of the quasi-conformal maps I have created using circle packings, demonstrate some of the interactive map features and discuss how these maps are expected to assist in understanding brain function.