According to its website (at the time of writing), the British Museum has five loan exhibitions touring across the world.

One is in North America (The Printed Image in China, 8th-21st Century, at the Metropolitan in New York), one in China (Passion for Porcelain: Masterpieces of Ceramics from the British Museum and the Victoria and Albert Museum, at the National Museum of China in Beijing) and one in Japan (Journey Through the Afterlife: The Ancient Egyptian Book of the Dead, at the Mori Arts Centre in Tokyo). Two, meanwhile, are in Australia: an exhibition devoted to ancient Mesopotamia in Melbourne and in Brisbane one, again, about that other great centre of early civilisation in Egypt.