This chapter is on the fences, boundaries and structures that lurk in and complicate the ethical globalism or cosmopolitanism of a range of global and human histories from the twentieth- and twenty-first centuries by writers and the UNESCO history of mankind team led by Charles Moraze and Georges-Henri Dumont. This means that few people have thought through the conceptual and practical implications of exiting this idea in realising cosmopolitanism. Global history should include an overview of the entire history of humanity from a consistent global viewpoint. Global histories are expressions of a desire to exit the forms of training, expression, periodisation, scaling and so on that marked the histories made in a conflict-ridden, unequal and local-looking world. Supporters of cosmopolitan ethics commonly argue for the removal or opening up of structures and boundaries in the service of the creation of a just, fair and peaceful world, but few endorse or manage their removal altogether.