The study of whole-brain functional brain connectivity with functional magnetic resonance imaging (fMRI) has been largely based on the assumption that a given condition (e.g., rest or task) can be evaluated by averaging over the entire experiment. In actuality, the data are much more dynamic, showing evidence of time-varying connectivity patterns, even within the same experimental condition. In this paper, we review a family of blind-source separation (BSS) approaches that have proven useful for studying time-varying patterns of connectivity across the whole brain. Initial work in this direction focused on time varying coupling among data-driven nodes, but more recently time-varying nodes have also been considered. We also discuss extensions of these approaches including transformations into the time-frequency domain and others. We also provide a rich set of examples of various applications that yielded new information about the healthy and the diseased brain. In sum, due in large part to developments in the field of signal processing, the fMRI community has seen a major new development in the development of approaches that can both capture whole-brain systemic connectivity information (connectomics) while also allowing this system to evolve over time as it naturally does (i.e., chronnectomics).