Emotion and executive control are often conceptualized as two distinct modes of human brain functioning. Little, however, is known about how the dynamic organization of large-scale functional brain networks that support flexible emotion processing and executive control, especially their interactions. The amygdala and prefrontal systems have long been thought to play crucial roles in these processes. Recent advances in human neuroimaging studies have begun to delineate functional organization principles among the large-scale brain networks underlying emotion, executive control, and their interactions. Here, we propose a dynamic brain network model to account for interactive competition between emotion and executive control by reviewing recent resting-state and task-related neuroimaging studies using network-based approaches. In this model, dynamic interactions among the executive control network, the salience network, the default mode network, and sensorimotor networks enable dynamic processes of emotion and support flexible executive control of multiple processes; neural oscillations across multiple frequency bands and the locus coeruleus-norepinephrine pathway serve as communicational mechanisms underlying dynamic synergy among large-scale functional brain networks. This model has important implications for understanding how the dynamic organization of complex brain systems and networks empowers flexible cognitive and affective functions.