In this article, we systematically review the current literature on neural connectivity and dynamics, or equivalently, structure and function. In particular, we discuss how changes in the connectivity of a neural network affect the spatiotemporal network dynamics qualitatively. The three major criteria of comparison are, first, the local dynamics at the network nodes which includes fixed point dynamics, oscillatory and chaotic dynamics; second, the presence of time delays via propagation along connecting pathways; and third, the properties of the connectivity matrix such as its statistics, symmetry, and translational invariance. Since the connection topology changes when anatomical scales are traversed, so will the corresponding network dynamics change. As a consequence different types of networks are encountered on different levels of neural organization.