Mapping the microscopical organization of the human brain provides an important basis for multimodal brain atlases, and is indispensable for linking functional, physiological, connectivity, molecular, or genetic properties to their cellular correlates. The BigBrain (Amunts et al., 2013) is a 3D model of a complete human brain at microscopic resolution, constructed from more than 7000 histological sections at a resolution of 20 micron isotropic. By resolving cortical layers, subcortical nuclei, and even larger individual cell bodies, it has enabled a new generation of high-resolution studies. Yet, the resolution of 20 micron is not sufficient to perform classical cytoarchitectonic mapping in arbitrary cutting planes, or quantitative analysis of 3D distributions and numbers of individual cell bodies. For such types of analyses, the construction of 3D brain model at the resolution of 1 micrometer is mandatory. While recent technologies in high-throughput microscopic imaging, large-scale storage, and high-performance computing have brought such an endeavour into sight, several challenges need to be addressed to compute such a model. These range from distributed data management to new image registration paradigms, very large numerical optimization problems, to cloud technologies for providing remote access to image data in the Petabyte range. In this talk, we will describe some of these challenges and recent progress on feasible solutions.