Abstract The study of fluctuations in time-resolved functional connectivity is a topic of substantial current interest. As the term “ dynamic functional connectivity” implies, such fluctuations are believed to arise from dynamics in the neuronal systems generating these signals. While considerable activity currently attends to methodological and statistical issues regarding dynamic functional connectivity, less attention has been paid toward its candidate causes. Here, we review candidate scenarios for dynamic (functional) connectivity that arise in dynamical systems with two or more subsystems; generalized synchronization, itinerancy (a form of metastability), and multistability. Each of these scenarios arise under different configurations of local dynamics and inter-system coupling: We show how they generate time series data with nonlinear and/or non-stationary multivariate statistics. The key issue is that time series generated by coupled nonlinear systems contain a richer temporal structure than matched multivariate (linear) stochastic processes. In turn, this temporal structure yields many of the phenomena proposed as important to large-scale communication and computation in the brain, such as phase-amplitude coupling, complexity and flexibility. The code for simulating these dynamics is available in a freeware software platform, the “Brain Dynamics Toolbox”.