This chapter provides a synthetic review of a long-term effort to produce an internally consistent theory of the neural basis of human cognition, the Leabra cognitive architecture, which explains a great deal of brain and behavioral data. In a highly influential commentary, Allen Newell first issued a call for a more comprehensive, principled approach to studying cognition, saying “You can’t play 20 questions with nature and win.” His point was that cognition, and the brain that gives rise to it, are too complex and multidimensional a system for a series of narrowly framed experiments and/or models to succeed in characterizing it. Instead, a single cognitive architecture should be used to simulate a wide range of data at many levels in a cumulative manner. However, these cognitive architectures tend to be complex and difficult to fully comprehend. In an attempt to most clearly and simply present the Leabra biologically based cognitive architecture, the authors articulate 20 principles that motivate its design at multiple levels of analysis.