The overriding spirit of the revival appears to be the familiar motto: Don’t mess with success. Once again, the production is directed by Trevor Nunn, with sets and costumes by John Napier. Once again, a Broadway theater has been transformed into a grungy London junkyard, where trash piles up against the walls and spills out into the auditorium — albeit on a somewhat smaller scale. That levitating tire, as famous a set piece as a certain falling chandelier, presides once again at the back of the stage. (Apparently the license plate on the battered car, which reads “NAP 70,” is an in-joke indicating how many productions Mr. Napier has designed. Imagine how many leg warmers have been involved.)

The most significant nod to the intervening decades and changing tastes is the hiring of Andy Blankenbuehler — the Tony-winning choreographer of “Hamilton,” the newest now-and-forever musical (to borrow the marketing slogan from the first “Cats”) — to groom the original choreography by Gillian Lynne. (Ms. Lynne gave an interview to the website and newspaper The Stage in which she said she felt positively murderous at this betrayal.)

With its thread of a plot, about which feline will be chosen by the lord of the cat kingdom, Old Deuteronomy (an aptly august-acting Quentin Earl Darrington), to ascend to something called the “Heaviside Layer” on the night of the annual “Jellicle Ball,” “Cats” is basically a series of divertissements. The felines prance and romp and occasionally hiss at one another as they introduce themselves in songs that provide the show’s greatest allure, as well as its variety.

Mr. Lloyd Webber is a musical magpie who can compose soaring pseudo-classical music as smoothly as he can jaunty music-hall-style jingles or jazz-inflected rock songs. His dexterity as a composer has never been more vividly showcased as it was, and is, in “Cats.” (His “School of Rock,” with a zesty pop-rock score, is currently installed at the Winter Garden Theater, the original “Cats”-box.)

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