How and why functional connectivity (FC), which captures the correlations among brain regions and/or networks, differs in various brain states has been incompletely understood. I review high-level background on this problem and how it relates to 1) the contributions of task-evoked activity, 2) white-matter fMRI, and 3) disease states in Chapter 1. In Chapter 2, based on the notion that brain activity during a task reflects an unknown mixture of spontaneous activity and task-evoked responses, we uncovered that the difference in FC between a task state (a naturalistic movie) and resting state only marginally (3-15%) reflects task-evoked connectivity. Instead, these changes may reflect changes in spontaneously emerging networks. In Chapter 3, we were able to show subtle task-related differences in the white matter using fMRI, which has only rarely been used to study functions in this tissue type. In doing so, we also demonstrated that white matter independent components were also hierarchically organized into axonal fiber bundles, challenging the conventional practice of taking white-matter signals as noise or artifacts. Finally, in Chapter 4, we examined the utility of combining FC with task-activation studies in uncovering changes in brain activity during preclinical Alzheimer's Disease (mild cognitive impairment (MCI) and subjective cognitive decline (SCD) populations), based on data collected at the Indiana University School of Medicine. We found a reduction in neural task-based activations and resting-state FC that appeared to be directly related to diagnostic severity. Taken together, the work presented in this dissertation paves the way for a novel framework for understanding neural dynamics in health and disease.