On July 15, Rembrandt Harmensz, van Rijn celebrated his 400th birthday. The fact that he died in 1669 should not dissuade us from lighting candles, cutting cake, and raising a glass to the Dutch titan: There is plenty to celebrate.

Three shows in New York of works on paper highlight Rembrandt’s extraordinary genius. An exhibition of approximately 50 drawings and prints and a dozen works by the master’s students is on view at the Metropolitan Museum of Art, and two shows featuring Rembrandt opened on his birthday at the Morgan Library & Museum. Installed back to back in a single spacious gallery at the Morgan, one show comprises roughly 50 Rembrandt prints; the other exhibition, “From Rembrandt to van Gogh: Dutch Drawings From the Morgan,” is packed with approximately 40 works and kicks off with four Rembrandt drawings.

Our usual Rembrandt fare in New York, though not without merit, is rather focused. The spectacular Rembrandt paintings in the Frick and the Met present us primarily with Rembrandt the portraitist. Although these portraits are full and rich and compelling (as great, frankly, as portraiture gets), Rembrandt was so much more.

The Morgan and the Met have each brought together stupendous groupings of prints and drawings, including nudes, landscapes, Biblical and historical scenes, sketches of everyday life, portraits, and self-portraits. Together with the Met’s dozen or so paintings — including “The Toilet of Bathsheba” (1643) and “Aristotle With the Bust of Homer” (1663) — and the Frick’s “Self Portrait” (1658) and “The Polish Rider” (c. 1655), the works currently on view in the city amount to an impressive, albeit print-heavy, retrospective of the phenomenon that is Rembrandt.

Rembrandt single-handedly revived the medium of etching in the 17th century, imbuing his black-and-white prints with an astonishing range of pressure, line, tone, light, and color — often all within a single image. Rembrandt was also one of the most innovative, courageous, and forthright of artists. He was a mystic, a visionary, and a village recorder.

Nearly all of the works on view in these three exhibitions are emotionally and psychologically rich masterpieces. Almost all inspire awe and amazement; some made me laugh out loud. The Met and the Morgan, which together bring it all to the table, celebrate Rembrandt’s entire spectrum — from soaring angels to wallowing hogs.

In terms of drawings and prints, all of the rarities and greatest hits have been brought out of the dim light of storage. Both the Met and the Morgan are featuring “The Death of the Virgin” (1639), “The Hundred Guilder Print” (1649), various states of “The Three Crosses” (1653–55), and the very early tiny portrait of the artist’s mother, in which her head is transformed into a mountain.

Also on view are numerous self-portraits, early to late, that show Rembrandt as child, sovereign, lunatic, and lion. In addition, the Met is showing a red-chalk drawing after Leonardo’s “Last Supper”; “The Good Samaritan” (1635), which focuses attention on a defecating dog; and a satirical drawing about art criticism that gives donkey ears to a critic and makes fools of clamoring connoisseurs. A tiny print at the Morgan, “The Monk in the Cornfield” (c. 1646), shows a woman and a monk copulating in a grove of trees as a farmer swipes at his field with a scythe.

But two small Met drawings, both titled “Elsje Christiaens Hanging on the Gibbet” (1664), and a small, mysterious print at the Morgan titled “Reclining Woman” (1658) rocket both exhibitions into the must-see stratosphere.

The Morgan’s “Reclining Woman” is a dark, velvety, French or Italianate odalisque seen from behind.Worthy of Ingres or Titian, it is one of Rembrandt’s most erotic images, up there with the Louvre’s “Bathsheba at Her Bath” (1654). It is the first image you see as you enter the Morgan’s show, and it holds from across the room.

Both versions of “Elsje Christiaens on the Gallows” depict the same woman hanging from the gallows. An eyewitness, Rembrandt drew them on the site of her execution. One drawing, in frontal view, rather straightforwardly presents the condemned woman; crumpled and tied to the post, she hangs lifelessly with the ax (the weapon of her crime) dangling next to her. The second drawing, in profile view, shows the ax seemingly embedded in her chest, as if the weapon, not the ropes, held her to the gallows and was the instrument of her death.

Many Rembrandt prints are on view at both the Met and the Morgan in the same or differing states, and the repetitions are enlightening: They present you with the opportunity for close comparison. In the hands of someone as great as Rembrandt, even a slight shift in a print’s light, tone, or density can considerably alter the image’s emotional timbre. If you see these shows consecutively, as I did, you may be surprised at how markedly one print at the Met, taken from the same plate, differs from one belonging to the Morgan.

These exhibitions also offer a chance to see how Rembrandt evolved an image over time — as in the various states of “The Three Crosses” (1653–55) or in “Christ Presented to the People” (1655). And they allow us to see how one impression differs from another, or how a change from white to an almost translucent Japanese paper or vellum can affect the image.

The Met’s impression of “Landscape With Three Trees” (1643) is darker than that at the Morgan, in which you can see more easily the two entwined lovers by the shore in the lower right of the image. Also, the Morgan’s “Portrait of Jan Six” (1647), a second state on Japanese paper, is warmer than the Met’s version, which is state four of four and on white paper.

Works on paper come out of hiding very rarely, and now is the time to become reacquainted with Rembrandt the draftsman and printmaker. It is also an excellent opportunity to get to know the subtly shifting nature of printmaking itself.

Seeing all of these Rembrandt drawings and prints next to those by contemporary and later Dutch artists makes it startlingly clear that few of Rembrandt’s countrymen, save van Gogh, came anywhere near his benchmark. (Vermeer is not on view.) Rembrandt’s consistent candidness and fearlessness, coupled with his astounding range and ability to reach inside his subjects (whether they were portraits or crucifixions) and lay bare everything that is essential — all bathed in impossibly beautiful, downy light — have rarely been equaled, and never surpassed.

Until October 15 at the Metropolitan Museum of Art (1000 Fifth Avenue at 82nd Street, 212-535-7710). Until October 1 at the Morgan Library & Museum (225 Madison Avenue, between 36th and 37th Streets, 212-685-0008).