The parental advisory-labeled music video, starring Cardi B as a naked rampage killer facing a trial, marked her directorial debut.

[2] She shared the cover art of the single, which features her escorted out of a court room entirely naked by a group of men with paparazzi taking pictures of her.

[5] "Press" received generally positive reviews from critics, with many noting the evolution of the rapper's attitude towards the media in the lyrics from previous songs such as "Bartier Cardi" and her featured verse on husband Offset's single "Clout"; NME called the song "defiant",[6] while Billboard labelled her as "pressing on" amid "bad press, haters, beefs".

[7] Pitchfork praised Cardi being "now fully ready to take aim at any haters" while noting the deviation between "non-stop cut-downs" and "goofier boasts about her money and sexual prowess"; the magazine also stated that the rapper had "sharpened her rapping abilities to deadly effect" in the song.

[15] Introduced by Drake, Cardi B opened her set at the 2019 OVO Fest performing "Press".