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The circuit connectivity of neurons underlies the capabilities of brains, and is important to understand for answering fundamental scientific questions, understanding brain disorders and engineering intelligent machines. Yet after a century of intensive research, comprehensive knowledge about brain circuits for any vertebrate is lacking, including the most widely studied laboratory organisms. This talk will discuss efforts to close this knowledge gap for the Mouse (http://mouse.brainarchitecture.mouse) and in the Marmoset. The second part of the talk will focus on methods from statistical physics applied to problems in machine learning to delineate algorithmic phase boundaries at which qualitative changes in performance take place. Such "big data phase transitions" are relevant for current technology applications, and may also have relations to the architectural principles of neural circuits.