In the 70 years since Guilford used his presidential address at the APA to launch the scientific investigation of creativity, we have learned a great deal about how to define creative achievements, identify creative individuals, and examine the associated psychological and physiological processes. This presentation summarizes work conducted at the Tennenbaum Center for the Biology of Creativity at UCLA, including studies of non-human species, studies of “free range” humans (not selected specifically for their creative achievements) and studies of humans who manifest “Big C” or exceptional creative achievement. These studies have used a range of methods including basic genetic strategies in rodents and birds, and studies of personality, neuropsychological functions, brain function and brain structure in humans. Hypotheses about specific cognitive operations important for creativity, including working memory, response inhibition and response generation, have provided a translational framework for these studies. A conceptual superstructure that we have termed the “edge of chaos” theory helps integrate findings across levels of analysis from the genetic through physiological properties of neural activation states to network operations and associated cognitive and behavioral processes. The neuroimaging findings reveal functional network dynamics linking exceptional creativity to increased randomness rather than more efficient “small world” networks, perhaps providing a substrate that enables “blind variation” prior to “selective retention” following Simonton’s “BVSR” model of creativity. The findings from the Tennenbaum Center are examined in the context of other empirical studies about the genetic transmission of traits associated with creativity, and recent conceptualizations about the “connectome landscapes” that are associated with vulnerability to or resilience in the face of perturbations, as a function of the efficiency of integration and the costs of modular organization. The presentation then examines implications of these findings and theories for understanding the relations of creativity with mental health, and for training human creative potential.