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Spontaneous fluctuations are a hallmark of recordings of neural signals, emergent over time scales spanning milliseconds and tens of minutes. However, investigations of intrinsic brain organization based on resting-state functional magnetic resonance imaging have largely not taken into account the presence and potential of temporal variability, as most current approaches to examine functional connectivity (FC) implicitly assume that relationships are constant throughout the length of the recording. In this work, we describe an approach to assess whole-brain FC dynamics based on spatial independent component analysis, sliding time window correlation, and k-means clustering of windowed correlation matrices. The method is applied to resting-state data from a large sample (n = 405) of young adults. Our analysis of FC variability highlights particularly flexible connections between regions in lateral parietal and cingulate cortex, and argues against a labeling scheme where such regions are treated as separate and antagonistic entities. Additionally, clustering analysis reveals unanticipated FC states that in part diverge strongly from stationary connectivity patterns and challenge current descriptions of interactions between large-scale networks. Temporal trends in the occurrence of different FC states motivate theories regarding their functional roles and relationships with vigilance/arousal. Overall, we suggest that the study of time-varying aspects of FC can unveil flexibility in the functional coordination between different neural systems, and that the exploitation of these dynamics in further investigations may improve our understanding of behavioral shifts and adaptive processes.