Here's a sampling of what they had to say:
William Stevenson in his Broadway.com Review: "Given the title, one might reasonably expect Gabrielle Lansner's new musical to be a Tina Turner greatest-hits collection. Think again. Although Lansner captures the singer's indomitable spirit with exuberant choreography, she sets the routines to original songs by Philip Hamilton. Fortunately, his best songs sound quite a bit like hard-driving '60s R&B, and the all-female cast dances with abandon. The show loses steam during the slower, abstract modern-dance numbers, but overall River Deep is a lively homage to a great entertainer and survivor."
Frank Scheck of The New York Post: "That River Deep: A Tribute to Tina Turner offers not a note of its subject's music is both its biggest weakness and its biggest strength. The music/theater homage that opened this weekend, directed and choreographed by Gabrielle Lansner, at times manages to convey the pop diva's forceful personality and musical impact while avoiding clichéd jukebox-musical renditions of the songs that made her famous. Still, there's something disconcerting about a production celebrating one of pop's most influential figures that ignores her music. Instead of such classics as "What's Love Got to Do With It" and the song that gives this show its title, the choreography is performed to an original score by Philip Hamilton that's clearly been influenced by Turner's blending of pop, soul and rock… .Visually, the piece is monotonous as well, with the sole diversion being backdrop projections of still pictures of the dancers. It isn't until the end that we see a photo of the subject herself, and by then it's possible that we may have forgotten who the show is supposed to be about."