Carl Kostyál opened his eponymous gallery at no. 12A Savile Row, London W1 in 2010 after a decade of private dealing and advising. He launched his first Stockholm space, Isbrytaren, at Igeldammsgatan 20, Stockholm in 2013 and in 2016 moved to the former German Embassy at Artellerigatan.

In May 2021 the gallery opened a new exhibition space, Hospitalet, in the 18th century mental asylum formerly known as Danvikens Hospital in Nacka, Stockholm, in collaboration with Gullringsbo Konstsamling.

In addition to the London and Stockholm programme, Kostyál commissions artist projects at his home in Milan.

The gallery regularly stages offsite exhibitions in the UK and Sweden. It runs invitational artist residency programmes at Masseria Fontana di Vite, Matera and, in collaboration with artist Canyon Castator, at Mohilef Studios, Los Angeles. Each summer Kostyál hosts an invitational Draw Jam in the south of Italy.