Redesigning an American museum’s Asian wing is no mean feat. How to convey the very real throughlines that make terms as broad as “Chinese art” and “Japanese art” meaningful, while also doing justice to the staggering variety of these ancient, and hugely populous, cultures? And what if you are also, like every other museum, under pressure to demonstrate the relevance of your antique artifacts to the present moment?

The Brooklyn Museum, a leading collector of Asian art for more than a century, satisfies these thorny curatorial problems about as well as anyone could in the virtuosic new reinstall of its Japanese and Chinese exhibits. (“Arts of Korea,” with a fascinating array of stark, monochrome ceramics including an 800-year-old sea-green cup with a scalloped rim, opened in 2017; sections on South Asian, Southeast Asian, Buddhist, and Himalayan art are still to come.)

Contemporary pieces, including some of the 50 paintings and sculptures by Chinese or Chinese-descended artists the museum has acquired in the last five years, are now integrated into brisk historical surveys, while a specially commissioned work by the Chinese artist Xu Bing, a curious mash-up of Chinese calligraphy and the Roman alphabet, occupies its own room. Not all this contemporary work is equally strong. But altogether the curators have succeeded in pulling five millenniums of art into a single, thrilling conversation.