Critics characterize the bar as "filthy", "seductive", and "alluring",[2] noting that it is an unusual find in the United States and bears resemblance to European red-light district establishments.

[1][3] New York magazine describes the venue as having "a rollicking backroom sex scene",[4] while the main room features theme parties, go-go dancers and DJs.

[1] It is owned by Allan Mannarelli, a straight proprietor who also operates Albion, a bar in Kips Bay, and who used to manage Superdive, a now-closed establishment in the East Village.

[10] Throughout the 2010s, The Cock was managed by Nashom Wooden, a fixture of the New York City nightlife scene who performed in drag as Mona Foot and was a member of the Ones.

Police responding to the incident entered the premises, and they issued summonses for sexual exposure by the venue's go-go dancers.

Mannarelli resolved to reopen the 93 Second Avenue location during New York City's 2021 Pride week,[15] at which time it was announced that the bar would require proof of vaccination against COVID-19 for entry.

[16] A May 2021 Queerty article indicated that, later in the year, Mannarelli intended to "spruce up an unused space [inside that location] and open it as the Celebration Room" in honor of Wooden, who died of a suspected case of COVID-19 in March 2020.

The Cock's reputation with patrons and critics is one of a raunchy, uninhibited space; some comment that it contrasts with the "corporate sterility" of New York and that similar venues are not common in the United States.

[17] In a list titled "The Absolute Best Gay Bar[s] in Manhattan", Mike Albo of GrubStreet.com ranked The Cock second with the following remark: "Rough-edged, covered in band stickers, and carved with little weird nooks and dark corners, this place is like a filthy, seductive, alluring alleyway.

The dearth of uptown attitude (or any apparent concern for cleanliness) pulls artists, musicians, writers, fashionistos [sic], tourists and closeted rebels, all of whom can appreciate a little dirty fun.