The brain is a complex dynamical system in which many different areas interact to process information in support of adaptive cognition and behavior. Just as brain areas vary in their local anatomical features and patterns of connectivity to remote regions, so too do their dynamics, and regional differences in intrinsic dynamics are a fundamental feature of functional brain organization. Here, I present the results of three studies which use resting fMRI to investigate how multiple features of intrinsic regional dynamics vary across the human brain, their relationship to the anatomical and connectomic properties of each area, and the extent to which these dynamics are disrupted in patients with focal brain lesions. First, I show that a key property of intrinsic regional dynamics—their timescale—is related to the topological role of each region within the modular community structure of functional and structural brain networks, and that cortical areas exhibit preferential functional connectivity to other regions with similar timescales. Second, I use a data driven time series “phenotyping” approach to characterize how multiple aspects of intrinsic dynamics vary across the cerebral cortex. I find that regional BOLD dynamics can be modeled as varying a long two spatial axes, each of which captures different time series features, and which exhibit distinct relationships to anatomical and connectomic hierarchies. Finally, given findings from my first two studies which suggest a robust relationship between regional timescales and network topology, I investigate whether alterations in network topology following focal brain lesions are associated with parallel alterations in the timescale of intrinsic dynamics. While I did not find the predicted effect, I nonetheless extend my findings from the first two studies by showing that timescales are related to multiple features of regional network topology both within and across individuals. Together, these results provide important new insights into a key feature of functional brain organization.