This introduction lays out the argument that an exploration of Muslim mobility and diversity across Asian history can help identify coercive dimensions that are often elided in dominant modern visions of ‘cosmopolitanism’. Starting with a discussion of the role that images of the premodern Muslim kingdom of al-Andalus in Spain have played in Muslim memory as a marker both of nostalgia and loss, the introduction then transitions to Asia. Specifically, the chapter traces how Islamic ideas of pilgrimage, migration, and learning shaped imaginaries of movement and of ‘opening’ frontier space defined as much by agonistic confrontation as by accommodation. These conceptual reflections build upon references to particular histories and historiographies of cosmopolitanism - including debates on the Indian Ocean, Sufism, religious ‘conscience’, and the global ‘umma’. Finally, this discussion sets the stage for the volume chapters to follow on coercion, asymmetrical power relations, and cosmopolitanism across diverse Asian Muslim societies.