Like a Faberge egg or an antique music box, Wes Anderson’s “The Grand Budapest Hotel” is a delight to the eye, intricately designed and flawlessly crafted. Bu also like such artifacts, it carries a strong aura of nostalgia for past eras more elegant and graceful than the coarse and brutal modern age. In doing so it shows a streak of tenderness and melancholy to go along with Anderson’s characteristic whimsy and wit, and thus continues the writer-director’s departure from mere preciousness that began with the enchanting “Fantastic Mr. Fox” and the lovely “Moonrise Kingdom.”

The film’s tone can be partially explained by the inspiration of Viennese author Stefan Zweig, whose work epitomized the old world but who was forced to flee Austria after the Anschluss, eventually committing suicide in 1942 in grief over how the civilization he esteemed was collapsing around him. But it also owes a good deal to the work of Ernst Lubitsch, especially “To Be or Not to Be,” which found humor and sophistication even against the backdrop of the Nazi takeover of Poland.

Plot-wise, the picture is basically a zany caper centering on M. Gustave H. (Ralph Fiennes), the ultra-precise, supremely arrogant, incredibly articulate (and sometimes surprisingly foul-mouthed) concierge at the titular hotel—located in the non-existent state of Zubrowska somewhere in Eastern Europe—in 1932. But the narrative is twice removed from these wild events. The central story is introduced by a revered Zubrowskan author (Tom Wilkinson) in 1985, in a tape made during the epoch of communist bleakness. He recalls how, as a younger man (Jude Law) in 1968, he visited the hotel, meeting and dining with its peculiar owner Zero Moustafa (F. Murray Abraham), who—as the then concierge (Jason Schwartzman) confides—curiously insists on residing in a small servant’s room during his stays.

It’s Zero who relates the tale of M. Gustave, whom he served as a devoted lobby boy (Tony Revolori) three-and-a-half decades earlier. (It’s a perfect example of Anderson’s delicious attention to detail that he and cinematographer Robert Yeoman shoot the picture in three different aspect ratios according to the time in which scenes are set—the so-called ‘Academy’ ratio of 1:37:1 for the boxy thirties, widescreen 2:35:1 for 1968, and 1:85:1 for the eighties scenes. Movie buffs will eat the tactic up.)

While Gustave is a paternalistic martinet to the staff of the ornate establishment, it seems he’s also a sexual libertine, enjoying all sorts of assignations. He’s especially partial to rich, elderly women like octogenarian Madame D. (an almost unrecognizable Tilda Swinton). So taken with Gustave is the dowager that when she expires—leading Gustave, with Zero in tow, to go to her estate in order to pay their respects—the reading of her will by lawyer Kovacs (Jeff Goldblum) reveals that she’s left the concierge a supposedly priceless painting called “Boy With Apple” (attributed to one Johannes Von Hoytl the Younger).

Of course her son Dmitri (Adrien Brody) will not hear of this, so with the connivance of the late woman’s butler Serge X. (Mathieu Amalric) Gustave absconds with the masterpiece, leading Dmitri to send the family’s brutal enforcer Jopling (Willem Dafoe) to retrieve it and settle scores with Gustave. That leads to a madcap pursuit also involving Captain Henckels (Edward Norton) of the proto-fascist military police (with a character name certainly meant to recall Hynkel of Chaplin’s “The Great Dictator”); a prison break led by a brooding convict named Ludwig (Harvey Keitel); the intervention of a secret society of master concierges (among whose members are Bill Murray, Bob Balaban, Fisher Stevens, Waris Ahluwalia and Wally Wolodarsky); a surrealistically funny ski-and-toboggan chase, ending with a homage to Hitchcock’s “North by Northwest”; and a gun battle at the hotel itself.

Along the way Zero proves endlessly supportive of his boss, as does his girlfriend Agatha (Saoirse Ronan), a beauty even if she does have a most peculiar facial birthmark. Most of what transpires is amusing in the skewered tone typical of Anderson, but there are numerous moments—a nasty interrogation in a railway car, a chase through a darkened museum—that take on a distinctly dark, sinister feel, and others—Zero’s recitations of his own childhood and of the eventual fate of Gustave and Agatha—that are abruptly poignant, causing the chuckles to catch in your throat. They remind us that while the film is essentially a lark, it’s one set at a time when the old European civility the film recreates in fairy-tale style was being undermined by new, very ugly forces that would blossom as the century wore on.

Thus while “The Grand Budapest Hotel” is mostly as light, airy and delectable as the pastries that play a small but important role in the plot, it has some layers with almost acidic bite. The cast respond to the various flavors expertly, especially Fiennes, who gives a beautifully controlled performances, bringing a subtly manic quality to Gustave and responding gleefully to the role’s myriad physical demands. Newcomer Revolori, with his charmingly deadpan style, makes a perfect sidekick for him. And though those two dominate, the supporting cast is almost uniformly superb as well. The only exceptions are Norton, a fine actor who looks more uncomfortable than callow, and Wilson, whose surfer-dude persona is at odds with his short stint as Gustave’s replacement near the close.

As important as the actors are the behind-the-scenes crew—production designer Adam Stockhausen, art directors Gerald Sullivan and Steve Summersgill, set decorator Anna Pinnock and costume designer Milena Canonero, along with the special and visual effects team—who outdo themselves in realizing Anderson’s fantastical, singular visions. A strong contribution also comes from composer Alexandre Desplat, whose eclectic score allows for passages of classical music, like Vivaldi’s mandolin concerti.

Visually “The Grand Budapest Hotel” represents an explosion of artifice, and one can simply immerse oneself in it and enjoy the accompanying stream of wit and slapstick. But it also possesses a strain of seriousness beneath the frothy exterior. In creating such a glitteringly unreal picture of a fabulous past, it doesn’t ignore the darkness that will overwhelm it. The combination makes for an extraordinary whole.