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 its new exhibition space, Hospitalet, in the 18th century mental asylum formerly known as Danvikens Hospital in Nacka, Stockholm, in collaboration with Gullringsbo Konstsamling.

In early 2020, Katharine Kostyál formally joined forces with her husband to co-run the gallery. Katharine was previously Curator at South London Gallery, Contemporary Art Specialist & Head of Sale at Christie's, London and latterly partnered with Jay Jopling at KK Art for White Cube, where she identified artists whose work had been rarely seen in the UK, researching, sourcing and curating exhibitions of their work at the London and Hong Kong galleries.

In addition to the gallery programme, Carl Kostyál commissions artist projects at the Kostyál home in Milan and stages offsite exhibitions, most recently at the Romantic castle of Stora Sundby in Sörmland, Sweden. It runs artist residencies in Italy and Los Angeles. Each summer the Kostyáls host an invitational Draw Jam in the south of Italy & regularly publishes artist monographs. The gallery runs a rolling Black Lives Matter Sponsorship Scheme, funding studies, providing work experience & industry connections for students each year.