Flow is a state of full task absorption, accompanied with a strong drive and low levels of self-referential thinking. Flow is likely when there is a match between a person's skills and the task challenge. Despite its relevance for human performance and the vast body of research on flow, there is currently still relatively little insight in its underlying neurocognitive mechanisms. In this paper, we discuss a set of large brain networks that may be involved in establishing the core dimensions of flow. We propose that dopaminergic and noradrenergic systems mediate the intrinsic motivation and activate mood states that are typical for flow. The interaction between three large-scale attentional networks, namely the Default Mode Network, Central Executive Network and the Salience Network is proposed to play a role in the strong task engagement, low self-referential thinking, feedback and feelings of control in flow. The proposed relationships between flow and the brain networks may support the generation of new hypotheses and can guide future research in this field.