Brains are large-scale networks consisting of millions of neuronal elements that are interconnected in characteristic patterns. These patterns of anatomical connections are critical for determining which neurons and brain areas can functionally interact. The activation of interconnected neuronal populations gives rise to global dynamical states that are associated with perception and cognition (Bressler, 1995; Frackowiak et al., 1997; Tononi and Edelman, 1998; Mesulam, 1998; McIntosh, 1999; Varela et al., 2001; Jirsa and Kelso, 2003; Ward; 2003). Given the importance of anatomical connections for generating structured neuronal dynamics, we need a deeper understanding of how anatomical connectivity and neuronal dynamics are interrelated. This chapter provides a brief overview of current concepts and models of how structured brain connectivity gives rise to complex neural dynamics. Our discussion will focus on recent results and simulations of the mammalian cerebral cortex.