Social interaction is central to the development of human cognition and behavior. Studying the neural mechanisms of social interaction helps reveal the neurobiological basis of social functions, such as group cooperation and knowledge transfer. In recent years, social neuroscience research has adopted hyperscanning technology and brain-to-brain coupling (BBC) measurements to reveal the group neural dynamics mechanisms under social interactions. Existing studies have primarily focused on three social contexts highly relevant to social interaction, namely interpersonal communication, task collaboration, and teacher-student instruction. However, the driving factors of BBC across these contexts and their interaction patterns under naturalistic paradigms have not yet been systematically analyzed within a unified framework, and the underlying driving mechanisms remain unclear. To address this limitation, the present review focused on three social contexts with increasing ecological validity in social interaction. It systematically examines the exogenous and endogenous drivers of BBC across these contexts and reveals commonalities and differences across contexts. Exogenous factors provide external conditions and spatiotemporal framework for interaction through sensory input and behavioral patterns. These external conditions induce BBC by guiding individuals to focus on the same target within the same time window, thereby invoking shared attention. However, exogenous drivers can only ensure surface alignment of interactions. Without the support of endogenous drivers, brain-brain coupling is difficult to maintain or deepen. Endogenous factors determine the depth and continuity of interactions through high-level social cognitive processing. Specifically, social closeness enhances trust and empathy between interacting partners, promoting interpersonal multimodal information integration and emotional empathy. Shared attention is the key link for individuals to move from behavioral alignment to initial coupling at the neural level. Shared intentionality led individuals to converge on goals and strategies, forming cognitive predictions during the cooperation process. Shared understanding ensures that individuals can perform high-level cognitive processing based on a common knowledge framework. The above-mentioned endogenous driving factors enhance BBC by engaging higher-order cognitive regions such as the prefrontal cortex, temporoparietal junction, and default mode network. This engagement enables the interaction to shift from transient attention coupling to stable intention alignment and cognitive sharing. Therefore, the formation of BBC can be viewed as a process that evolves "from external to internal, from weak to strong". Exogenous driving factors initiate neural alignment through shared attention. Endogenous driving factors then strengthen BBC via shared understanding and shared intentionality. Together, these processes support the construction of group-level shared cognition. Finally, this article summarized the current challenges in research on the driving mechanisms of BBC and provided an outlook for future development. First, it is necessary to theoretically establish a hierarchical model of brain-brain coupling based on a hierarchy of cognitive complexity, systematically distinguishing between the characteristics of BBC driven by low-level processes and higher-level interpersonal shared cognitive mechanisms. Second, at the methodological and technical level, future development of multimodal hyperscanning systems such as EEG-fNIRS and closed-loop hyper-transcranial alternating current stimulation could comprehensively analyze the dynamic evolution of BBC related to shared cognition in the temporal, spatial, and frequency domains. In summary, this article constructed a theoretical framework for the driving mechanisms of BBC across social contexts, hoping to provide a methodological basis for controlling the driving factors of naturalistic paradigms in social neuroscience research.