Traditionally, brain function is studied through measuring physiological responses in controlled sensory, motor, and cognitive paradigms. However, even at rest, in absence of overt goal-directed behavior, collections of cortical regions consistently show temporally coherent activity. In humans, these resting-state networks have been shown to greatly overlap with functional architectures present during consciously directed activity; this motivates the interpretation of rest activity as day-dreaming, free association, stream-of-consciousness, and inner rehearsal. For the same reason, it has been hypothesized that the rest-state networks are a unique property of humans. However, it has been shown in monkeys that similar coherent fluctuations are present during deep anesthesia at levels of no consciousness. This latter finding suggests that the emergence of rest-state networks represents a fundamental property of biological cortical organization, rather than a representation of consciousness. In this chapter we critically discuss the elements of spatiotemporal brain systems which may contribute to a functional brain architecture that supports the emergence of rest-state networks. In particular, we consider local versus global contributions to connectivity, time delays due to signal transmission, and noise. These parameters span a space in which “phases” of spatiotemporal brain dynamics are represented, not unlike the fluid, gas, and solid phases of water in a parameter space spanned by pressure and temperature. Specifically, we will argue that the brain operates in the proximity of instabilities separating two phases of brain operation. Our results indicate that “brain noise” transiently activates the subnetworks resembling rest-state activity, and gives rise to the dynamics observed with associated mental processes.