After an unsuccessful attempt at a career as a jazz singer, Kulig enrolled at the AST National Academy of Theatre Arts in Kraków, graduating in 2007.

On television, she played the lead role in the sitcom O mnie się nie martw (2014–2018), and starred in the Netflix series The Eddy (2020).

[10] After four years of studies, she earned an acting degree with a specialisation in singing from the AST National Academy of Theatre Arts in Kraków in 2007.

[1] In 2006, while still in drama school, she made her stage debut as Hermia in the play A Midsummer Night's Dream at the Helena Modrzejewska National Old Theatre in Kraków.

[15] In the film, set in Paris, she portrayed Ania, a Polish barmaid who falls in love with the protagonist American writer Tom Ricks (Ethan Hawke).

[16] In 2011, Kulig was also partnered with Juliette Binoche for Małgorzata Szumowska's drama Elles, similarly set in Paris, in which she played Alicja, a Polish economics student who moonlights as a prostitute.

Kevin Jagernauth of IndieWire opined that she "has the potential to be breakout star boasting a strong screen presence and an undeniable beauty".

[19][20] Aside from these two projects, 2011 saw Kulig appear in the war drama Remembrance,[21] and star in the Polish comedies: Los numeros, Million Dollars and Dance Marathon.

[25] Kulig received her second Polish Academy Award nomination for Best Supporting Actress for her role in Jacek Borcuch's drama Lasting, which premiered at the 2013 Sundance Film Festival and was described by The Hollywood Reporter as "fine-tuned on every level".

[1][30] Kulig next starred in the romantic comedies Sophie Seeks Seven (2014) and Warsaw by Night (2015),[31][32] and in the commercially successful films Disco Polo (2015) and Pitbull: Tough Women (2016).

[34][36][37] She also portrayed Sister Irena in Anne Fontaine's critically acclaimed 2016 World War II drama The Innocents inspired by the true story of Polish Catholic nuns who became pregnant from rape by Soviet soldiers stationed near their convent.

[15] The part of Zula, a woman in post-war Poland who joins a folk music touring group, was once again written by Pawlikowski with her in mind.

[40][41] Kulig was drawn to the role as it required her to sing and dance, allowing her to showcase her talents; she trained with a folk group for half a year in preparation for the part.

[42] Mark Kermode of The Observer wrote that she "delivers a star-making performance of astonishing range and depth",[43] and Mick LaSalle of San Francisco Chronicle stated that "she takes the role of a lifetime between her teeth, chomps on it, pounds it into the ground and never lets go for a second.

[9][52] Kulig starred as Polish jazz singer Maja in Damien Chazelle's 2020 Netflix musical drama series The Eddy.

"[59] In 2023, Kulig appeared in Rebecca Miller's romantic comedy She Came to Me alongside Peter Dinklage, Anne Hathaway, Marisa Tomei and Brian d'Arcy James.

[67] Kulig also had a supporting role in Michael Keaton's 2023 noir thriller Knox Goes Away,[68] and made a guest appearance in Apple TV+ 2024 miniseries Masters of the Air.

[70] In Masters of the Air, she played a Polish World War II widow who crosses paths with Major John "Bucky" Egan (Callum Turner) during his stay in London; a fan of director Cary Joji Fukunaga, she accepted the role as she wanted to work with him.

[71][72] Kulig is next set to portray Jolanta Wadowska-Król, a real-life Polish pediatrician who in the 1970s uncovered the problem of lead poisoning in children living near the Szopienice steelworks, in the upcoming Netflix series Ołowiane dzieci.