Brain circuitry processes information by rapidly and selectively engaging functional neuronal networks. The dynamic formation of networks is often evident in rhythmically synchronized neuronal activity and tightly correlates with perceptual, cognitive and motor performances. But how synchronized neuronal activity contributes to network formation and how it relates to the computation of behaviorally relevant information has remained difficult to discern. Here we structure recent empirical advances that link synchronized activity to the activation of so-called dynamic circuit motifs. These motifs explicitly relate (1) synaptic and cellular properties of circuits to (2) identified timescales of rhythmic activation and to (3) canonical circuit computations implemented by rhythmically synchronized circuits. We survey the ubiquitous evidence of specific cell and circuit properties underlying synchronized activity across theta, alpha, beta and gamma frequency bands and show that their activation likely implements gain control, context-dependent gating and state-specific integration of synaptic inputs. This evidence gives rise to the dynamic circuit motifs hypothesis of synchronized activation states, with its core assertion that activation states are linked to uniquely identifiable local circuit structures that are recruited during the formation of functional networks to perform specific computational operations.