Carl Kostyál established his eponymous gallery at 12a Savile Row, London, in 2010, followed by the opening of a second location in Stockholm in 2013. In May 2021, the gallery inaugurated a new 400-square-metre space in Stockholm at Hospitalet, a historic 18th-century former mental asylum. In May 2025, Kostyál opened its third location at Landmark South in Hong Kong.

Known for identifying talent and supporting artists in developing their careers internationally, Kostyál staged the first major European exhibitions of Gina Beavers, Szabolcs Bozó, Peter Coffin, Petra Cortright, Alex Da Corte, Sara Cwynar, Camilla Engström, Oli Epp, Al Freeman, Alexander Guy, Charles Harlan, Yu Honglei, Alex Israel, Austin Lee, Helen Marten, Gus Monday, David Ostrowski, Jon Rafman, Timur Si Qin, Gedi Sibony, Mandy El-Sayegh, Li Shurui, Emma Stern, Austyn Weiner, Wang Yuyang, Jess Valice and Zhao Zhao, among others.

Katharine Kostyál is co-owner and Director of Carl Kostyál gallery. She joined forces with her husband in early 2020 having previously founded and run KK Art at White Cube (2013 – 2020) in partnership with Jay Jopling. That venture saw her stage nine major solo exhibitions over the past six years at White Cube’s London and Hong Kong galleries. Identifying artists whom she judged to have unfairly fallen off the art world radar or whose oeuvre had not been shown previously in the UK but who were ripe for (re)presentation, she researched, sourced, acquired, curated and sold solo exhibitions of their most significant work. Her exhibitions include historic shows of Günther Förg, Minjung Kim, two with Dóra Maurer, Lee Seung- Taek, four with Park Seo-Bo and Peter Schuyff.

Beyond its London, Stockholm and Hong Kong programming, the gallery regularly stages off-site projects in various private locations in Europe. Since 2018, Kostyál has hosted an annual invitational Draw Jam, traditionally held in southern Italy, bringing artists from all over the world to spend time together and draw, culminating each time in an informal exhibition, after which the works are sold to raise funds for charity. In 2025, the Draw Jam took place in Luxor, Egypt, at the historic Al Moudira.

Kostyál maintains close relationships with several leading institutions, most notably the Albright-Knox Art Gallery in Buffalo, the Louisiana Museum of Modern Art in Denmark, and Moderna Museet in Stockholm. Over the past decade, he has facilitated and personally contributed more than thirty acquisitions to these and other institutions, among them major works by Joe Bradley, Alex Da Corte, Alex Israel, Helen Marten, Dóra Maurer, Rebecca Ness and Katja Novitskova.