The Swahili coast of eastern Africa is a Muslim cultural complex that is very much maritime oriented and a place of many crossroads. Its visual culture has confounded art and architectural historians. Where does it “belong” on the art historical map of the world? Is it African, Asian, or Islamic art? This talk revisits the 2019 exhibition World on the Horizon: Swahili Arts Across the Indian Ocean (curated by myself and Allyson Purpura), which used the Swahili coast as a springboard to consider what it means to see the world and its arts not in terms of borders of continents or nations, but in terms of migration and mobilities. I consider the exhibition’s critical reception, impact, and also its blind spots.