It so happens that our vague, pop-cultural notion of what Riverdance is — Irish step dancing to overproduced Celtic music by high-kicking men and women in tights — is basically right.

Step up · Riverdance, advertised as an international phenomenon, presents traditional Irish step dancing alongside Russian ballet and flamenco. The show is in its final run. - Photos courtesy of Broadway L.A.

And it’s fantastic.

Despite its relentless showiness and schmaltz, Riverdance is a soul-expanding experience that truly must be seen to be believed.

First performed in 1994, Riverdance has since become, to paraphrase its billboard advertisements, an international phenomenon, bringing its version of Irish culture to millions of people the world over. As part of the North American touring company’s farewell tour, Riverdance has returned to the Pantages Theatre for a brisk two-week engagement, ending Jan. 24.

There is an effort to structure the show so as to tell some sort of cultural story. Suffice it to say, that effort — mainly a series of pre-taped, faux-poetic narrations — fails miserably, but we couldn’t care less. This is pure celebration: two-plus hours of Irish music, dance and song that fly by effortlessly.

Although we leave with no new knowledge of Celtic mythology or Irish history and a feeling of being slightly talentless, we are nonetheless inspired, radiant and overjoyed by the experience.

The show’s two acts are separated by a 15-minute intermission. The first act is probably more satisfying than the second, which — except for a crowd-pleasing dance-off and some Russian ballet — is weighed down by comparatively staid numbers.

The best part of the show is “Firedance,” a flamenco solo by the beautiful Rocio Montoya. Bill Whelan’s music, which sometimes overpowers other performers, is expertly tamed by Montoya. She dances as though she were the instrument, each flick of her wrist the pluck of a fiddle’s string.

Lest we forget that the music is not coming from her but from other people onstage, the next number, “Slip into Spring – The Harvest,” features the phenomenal five-man Riverdance band, led by a plucky, charismatic Pat Mangan on the fiddle, who has probably spent much of his young life fighting off elderly women trying desperately to get their hands on his eminently squeezable cheeks. His technique is flawless, as is that of his fellow players.

It is the two principals (Marty Dowds and Melissa Convery), however, who carry the show. Thankfully, there is real chemistry between these world-class dancers and the unison sequences are properly epic. Convery has a carefree lightness to her movement, especially in her soft-shoe work, and an enchanting smile, which is complemented nicely by Dowds’ rigorous technique and straight-faced masculinity.

Other notables include baritone soloist Michael Samuels, whose perfectly controlled voice is so captivating we forget that the lyrics to these songs are unbearably mushy. His “Heal Their Hearts – Freedom” is one of the high points of the second act, thanks also to the timing of Rupert Murray’s mostly fluid lighting.

The dance-off is the other high point. Dowds and friends take on two street tappers (the nearly show-stealing Jason E. Bernard and Kelly Isaac) in a memorable battle that has the crowd cheering wildly. They continually have to exceed expectations, which becomes the basic theme of the night.

Most of the numbers either succeed or fail by comparison. After a point, we think we have seen this already, and it is up to the performers to surprise. Sometimes, as in the Russian ballet sequence, they do. Other times, as in Montoya’s second solo, “Andalucia,” which pales in comparison to her first, they don’t.

This is perhaps why the finale falls slightly flat as well. After a time, it turns into a greatest hits of the night, which is fun but obviously not fresh. Still, it rounds out the show.

Riverdance is nothing without the signature clickety-clack of the hard-shoe routines on the stage floor. Thankfully, the sound in the Pantages is better than ever. Michael O’Gorman’s sound design perhaps slightly over amplifies the band, but there is a fullness and crispness to the sound not heard in that hallowed chamber for some time. With one noticeable exception, the dancers were nearly perfectly synchronized in every number, and it paid off with the sound.

The backdrops are the only truly outdated part of the show. Old looking and muted, they do little to accent the performances. If they ever update Riverdance, they should start there.

Riverdance is a show everyone can and should see. When it ends, you leap to your feet — as much for yourself as for the performers onstage — and you find there is a little Irish jig in your step.