Two exceptional and extremely complementary shows of Japanese ukiyo-e woodblock prints, paintings, and illustrated books are currently available in New York. Together, they offer a phenomenal and thorough overview — a gathering of nearly 250 17th-, 18th-, and 19th-century works by master painters and printers such as Moronobu, Toyoharu, Utamaro, Hokusai, Kunisada, Hiroshige, and Kuniyoshi.

“Designed for Pleasure: The World of Edo Japan in Prints and Paintings, 1680–1860,” co-organized by the Asia Society and the Japanese Art Society of America, the show’s curator, is a two-part exhibition of approximately 150 works, primarily prints, paintings, and book illustrations. Japanese prints, like all works on paper, are light sensitive; because of this, the exhibition’s current grouping of works will be rotated out on April 4, when the second half of the exhibition will commence.

As with “Utagawa: Masters of the Japanese Print, 1770–1900,” “Designed for Pleasure” focuses on ukiyo-e (“pictures of the floating world”) of the leisure and pleasure centers — the theaters, brothels, restaurants, and teahouses — of then-isolated Edo, Japan (present-day Tokyo). Edo, with more than 1 million inhabitants, was for a time in the 17th and 18th centuries the world’s largest city, as well as Japan’s leisure and pleasure capital. “Designed for Pleasure,” which celebrates ukiyo-e, also illustrates the interrelationships among art, culture, and commerce that produced a renaissance of Japanese printmaking. The show explores the relationships among artists, publishers, poets, writers, theater owners, actors, geisha, courtesans, Zen Buddhism, mythology, and the modern, populist Kabuki (as opposed to the traditional Noh) theater — or what we might think of today as Japan’s version of Broadway.

A borough away, the Brooklyn Museum has mounted “Utagawa: Masters of the Japanese Print, 1770–1900,” a focused and straightforward exhibition of 95 ukiyo-e woodblock prints by more than 15 artists that traces the two-pronged lineage, beginning with Utagawa Toyoharu (1735–1814) and including his better-known student Utagawa Hiroshige (1797–1858), of the Utagawa School, one of the most important and influential groups of painters in Japan. The show, as with “Designed for Pleasure,” includes portraits of actors, courtesans, and beautiful women, as well as landscapes, seascapes, mythological scenes, views of bridges, Mt. Fuji, and the interiors and intimate activities of pleasure houses. Compact and beautifully interwoven, it presents the fascinating, complex, sometimes tightly knit, sometimes far-afield relationships among overlapping generations of artists. And it allows us to see masters alongside pupils, as well as stars alongside imitators, all within one family tree.

“Designed for Pleasure,” which is unusual in that it comprises both scroll paintings and prints, as well as albums, porcelains, fans, and firemen’s coats — including one smoky blue jacket in which demonic yellow storm gods tumble from bamboo scaffolding — is more heady, dreamy, various, and erotic than “Utagawa.” The Brooklyn Museum’s show does not lack for masterpieces and shunga (or erotica), but it presents a more ordered and less-titillating grouping overall. Although almost all ukiyoe printmakers considered themselves first and foremost painters (for the luxury class) and, second, printmakers (for the middle class), it is primarily through woodblock prints that the West became familiar with Japanese art in the 19th century — a fact to which these two mostly woodblock-print shows of works from American collections attests.

“Utagawa” is excellent and very informative in terms of artistic lineage. Drawn primarily from the renowned holdings of the Madison, Wis., Chazen Museum of Art’s Van Vleck collection of more than 4,000 Japanese prints, it is first-rate and thorough, and it includes a number of rarely seen images. At times, however, it feels anchored in scholarly pursuit (the 500 members of the Utagawa School) more than in aesthetic and other pleasures — which were, of course, what ukiyo-e was all about.

Organized at the Chazen Museum by Laura Mueller and at the Brooklyn Museum by Joan Cummins, “Utagawa” trails off with some mediocre work by Utagawa followers and, compared to “Designed for Pleasure,” can at times feel a little evenhanded, if not pedantic. That said, the pleasurable show offers unusual works such as prints, by Kuniyoshi, made after walls of graffiti that depict portrait heads of actors (prints that look like sketchbooks), as well as beautiful monochrome blue woodcuts and peculiar hybrid images of Americans who, though clearly Western, look and dress like Japanese. These exotic images, made after Japan was opened to trade with the West, yet before the Japanese had actually encountered many Westerners, illustrate how difficult it is to imagine, and then to depict, a people unlike you.

The lineage and richness of ukiyo-e — from the 17th-century black-and-white ink drawings up through the intricate full-color prints, which emerged in the late 18th century — as opposed to the rich lineage of a single artistic school, is the focus of the two-part “Designed for Pleasure.”

The show is divided into seven sections, each devoted to key figures, such as publishers and printers or, as with a section of works by Hiroshige, Kuniyoshi, and Kunisada, masters of ukiyo-e. It begins with a spectacular gallery of works by Hishikawa Moronobu (1630/31–1694), the acknowledged father of ukiyo-e, and Okumura Masanobu, who introduced new formats and coloring techniques. Moronobu’s black-and-white 55-foot scroll “A Visit to the Yoshiwara” (late 1680s), which depicts 15 episodes from a house of pleasure, is a tour de force of individual scenes stacked and connected as if links in a chain. Moronobu’s scenes of tumbling, frolicking lovers, folded in on one other and tied into whipping knots, are extremely acrobatic and erotic, and Masanobu’s “Courtesan in Robe Decorated With Calligraphy” (c. 1710s), in which the courtesan parts her kimono at her waist, exposing the inner folds of her robe — suggestive flowering swaths of bright red and stark white material — would make even Georgia O’Keeffe blush.

Masanobu’s “Courtesan” may not be the most delicately stated of the works on view in these exhibitions, but it is in keeping with the associative and metaphoric power of the greatest of these Japanese prints, such as Hokusai’s great waves, which culminate in white finials that suggest flocks of birds, can-can girls, and menacing tentacles. The most arresting works in both shows are the ones in which complicated jostling kimono patterns, beautiful and fully formed figures, architecture, and flowing nature all retain complete autonomy yet manage to merge metaphorically and to flow easily and rhythmically. What separates the masters from the merely competent is a mixture of subtlety, naturalism, dreaminess, and invention, in which ever-present chaos and unpredictable nature achieve a transcendent calm.

At the Brooklyn Museum, Toyoharu’s crowded lyrical street scenes and Kabuki theater interiors remain fully packed yet vast. This is also true of Masanobu’s depictions of the same themes. Their figures become cinematic — moving through space with a kind of Futurist progression, yet that space remains airy and elastic. Fluttering flags, branches, tails, and kimonos all echo one another, creating larger rippling arabesques that whip through and open up the prints’ compactness.

Yet some of the most startling of the images in “Designed for Pleasure” are the painted scrolls, including Hokusai’s “Five Beauties” (1805–13), in which a stacked accordion of zigzagging figures, as if a series of knotted silk scarves, suggest within the kimonos’ patterns interior spaces and atmospheres that are foggy, sanguine, or crystalline. In one, its deep blackness, decorated with white blossoms, opens like a starry sky over a sleepy village. In another miraculous painting by Hokusai, of a reclining courtesan (c. 1800), the poem on the painting reads: “Sometimes I turn into a cloud / like the smoke from tobacco I have lit, / other times I turn into rain / which makes a client linger a bit.” As with the forms in a Braque still life, she does appear to flit through various incarnations, including that of a landscape, a cloud, a bud, a leaf, smoke, rain, and the wind.

The greatest figures in these shows writhe. Their kimonos interlock, overlap, and intertwine. They twist like snakes, pool like water, and fall like rain. And there is a naturalism to the landscapes that is as serene as that in Corot. The best artists represented here are tender and delicate without sacrificing forcefulness and strength; they invent like madmen but never let us forget that their art is grounded in nature. The floating world is a pleasurable dream; but, thanks to these two exhibitions, it is a dream we can not only enter but hold onto.

“Designed for Pleasure”: Part 1, until March 30; Part 2, April 4-May 4 (Asia Society and Museum, 725 Park Ave. at 70th Street, 212-288-6400); “Utagawa”: until June 15 (Brooklyn Museum, 200 Eastern Parkway, 718-638-5000).