The Enigma show was complimented for its theatricality and Gaga's showmanship, although some reviewers found it disjointed, and deemed the narrative confusing and unnecessary.

The Jazz & Piano concerts were critically acclaimed – journalists found them a nostalgic throwback to the "Golden Age" of Las Vegas, and praised Gaga's vocal skills.

[3][4] In July 2018, Ticketmaster website had mistakenly uploaded details about a "2 Show Bundle" for the residency with tentative name as Enigma and ticket sales from the end of that month.

[6] Two different shows were listed with the press release, with Enigma described as a "brand-new odyssey of [Gaga's] pop hits built as an experience unlike any other,"[7] and Jazz & Piano painted as featuring stripped-down versions of her songs accompanied by tracks from the Great American Songbook.

Development of the residency took place while Gaga was promoting her 2018 movie, A Star is Born, therefore only a short amount of time was available for the creative process.

She wore a neon green tulle dress by designers Laurence & Chico, with latex gloves and a swim cap from Vex Clothing.

Matt Moen from Paper Mag felt that the poster hearkened back to Gaga's fashion choices during The Fame Monster (2009) era, suggesting the singer's return to avant-garde looks.

[13] On December 4, 2018, Gaga shared a video from the rehearsal on her Instagram account showing her in a bodysuit with dots on it, utilizing motion capture while the song "Aura" played in the background.

[19] Production designer LeRoy Bennett described the show as "a journey about Gaga and her Enigma character finding themselves within each other", therefore taking place "in various settings as she's going into her virtual world and her past.

[21] For the Enigma show, the main inspiration was sci-fi,[22] and the list of designers included Tom Ford, Asher Levine, and Vex Latex.

[21][23][24] The outfit was covered in tiny mirrors, with Out magazine's Glenn Garner noting that "given her nightlife roots, it’s fitting that she’s channeling a disco ball at the beginning of her show".

[21][23][24] A later look was an armor-inspired suit with light-up panels,[21][23] which received comparison to a Patricia Field costume "for a movie about a late '80s heavy metal singer".

[21][26] Designers who outfitted the Jazz & Piano shows include Ralph Lauren, Schiaparelli, Adrian Manceras, Armani Privé, and Gaga's sister, Natali Germanotta.

After an interlude, the singer returns on stage wearing a fluorescent suit and a manga inspired wig, and performs "Dance in the Dark" and "Beautiful, Dirty, Rich".

The last act opens with "Bad Romance", performed in a cream latex suit on the catwalk while Gaga's dancers execute the choreography on the main stage.

The singer's Jazz & Piano engagement does not involve a comprehensive narrative as the Enigma show, but it is divided into four segments, each of them preceded by costume change and black-and-white interlude films.

[35] Chris Willman from Variety called the Enigma show a "back-to-roots move for the superstar", as it focused on her "art and artifice of being spectacular", and complimented Gaga for singing live for its entirety.

"[18] John Katsilometes, from the Las Vegas Review-Journal praised the singer's vocal and piano skills, saying that "she is dazzling dancing around the stage, a slim figure in a mirrored one-piece to open the night, but her heartfelt playing on the keyboards shows she can move a crowd subtly, too.

[25] Paste Magazine's Garrett Martin found Enigma "one of the most proudly over-the-top concert extravaganzas I’ve ever seen", while adding that the show "doesn’t just overpower you with lights, music and pyrotechnics, but with a sense of pride and inclusivity", complimenting Gaga's "touchingly earnest and heartfelt performance".

"[40] Randy Lewis from the Los Angeles Times thought that Gaga was "in full pop star mode", and while he appreciated the "gigantic" set pieces and the inclusion of the singer's biggest hits, he found the show "disjointed", with "little sense of narrative flow".

He also added that the choreography "offers little in the way of physical expression or amplification of her songs’ lyrics or music", although he noted that it showcased "plenty of wild, kinetic energy".

[41] At Las Vegas Weekly, Leslie Ventura called Gaga "a perfectionist down to the smallest details, and her showmanship is unparalleled – her vocals, the costuming, the dancing, the hits."

[35] Mikael Wood from the Los Angeles Times also compared it to Enigma, saying that "for all their differences in style and repertoire, both shows feel indelibly Gaga, linked by the unifying force of her wacky personality and her raw vocal talent."

[32] John Katsilometes of the Las Vegas Review-Journal highlighted Gaga's vocal skills, saying she was "nailing several a cappella moments" during her jazz performances.

[20] For Nick Remsen at Vogue, "Jazz & Piano is entertaining, engaging, educational (thanks in part to black and white filmic interludes...), and astutely conceived for power and provocation without being overbearing.

"[28] Pre-sales for the show started on August 8, 2018, for Gaga's fan club members, followed by Citi bank credit card holders on the next day, getting an early chance at acquiring the tickets.