Attention network theory distinguishes three independent systems, each supported by its own distributed network: an alerting network to deploy attentional resources in anticipation, an orienting network to direct attention to a cued location, and a control network to select relevant information at the expense of concurrently available information. Ample behavioral and neuroimaging evidence supports the dissociation of the three attention domains. The strong assumption that each attentional system is realized through a separable network, however, raises the question how these networks relate to the intrinsic network structure of the brain. Our understanding of brain networks has advanced majorly in the past years due to the increasing focus on brain connectivity. The brain is intrinsically organized into several large-scale networks whose modular structure persists across task states. Existing proposals on how the presumed attention networks relate to intrinsic networks rely mostly on anecdotal and partly contradictory arguments. We addressed this issue by mapping different attention networks at the level of cifti-grayordinates. Resulting group maps were compared to the group-level topology of 23 intrinsic networks, which we reconstructed from the same participants' resting state fMRI data. We found that all attention domains recruited multiple and partly overlapping intrinsic networks and converged in the dorsal fronto-parietal and midcingulo-insular network. While we observed a preference of each attentional domain for its own set of intrinsic networks, implicated networks did not match well to those proposed in the literature. Our results indicate a necessary refinement of the attention network theory.