The track "Forever Young" was later promoted on Korean music programs and peaked at number two in South Korea.

Upon its release, Square Up debuted atop the Gaon Album Chart and went on to sell almost 179,000 copies in its first fifteen days of availability in South Korea.

[23][22] The closing track "See U Later" is a "cutting breakup" dance-pop song that mixes pop and hip-hop with a "trap-laden" chorus, "reminiscent" guitar sound and the distortion 808 bass.

[22] On the afternoon of June 15, Blackpink held a press conference for the release of "Square Up" at M-CUBE, Sinsa-dong, Seoul.

[26] On June 23, the group appeared as guests on JTBC's Idol Room to promote the EP, making their debut on the show.

Chase McMullen, writing for The 405, praised the album's "readymade hooks and airtight, bursting sonics" and its ability to go "from confrontational to blissfully ecstatic at the drop of a hat", proving Blackpink's mettle in the global K-pop boom.

"[34] Refinery29 placed Square Up at number 8 at their best K-pop albums of 2018, saying that it "shimmers with signature Blackpink cheekiness and effortless swagger, momentarily satiating the fans who are waiting for more.

[44][45] The lead single "Ddu-Du Ddu-Du" debuted as the highest-charting Hot 100 hit ever by an all-female K-pop act, opening at number 55 with 12.4 million US streams and 7,000 downloads sold in the tracking week ending June 21, 2018,[5] according to Nielsen Music, also entering on the US Streaming Songs tally at number 39, where Blackpink became the first K-pop girl group to chart a title.