The Shed is located in the Bloomberg Building, adjacent to the northern leg of the High Line elevated park, near the Chelsea gallery district.

[5] In May 2010, the Metropolitan Transportation Authority (MTA) leased the air rights over the rail yard for 99 years, at a price of US$1 billion to a joint venture of Related Companies and Oxford Properties Group, which built a platform above both the eastern and western portions of the yard on which to construct the buildings, including what was then known as the Culture Shed.

[6] In April 2013, the Related/Oxford joint venture obtained a $475 million construction loan from parties including Barry Sternlicht's Starwood Property Group and luxury retailer Coach.

[8] As part of the Hudson Yards rezoning plan, the city preserved a parcel of city-owned land on West 30th Street between 10th and 11th Avenues, adjacent to The High Line, for future cultural use.

Working closely with then Department of Cultural Affairs Commissioner Kate Levin, they determined the space "should be a highly flexible one that could cater to the growing desire of many artists to break out of their silos and blend disciplines".

[14] The city retains ownership of the land on which the Shed is built and provided Capital Grant funding for the project.

[20] Construction of the Shed over the West Side Yard, began after caissons were sunk to support a platform over the tracks.

The wraparound shell weighs 8 million pounds (3,600,000 kg), and is made of an exposed steel frame clad in a fluorine-based plastic called ETFE, which has the thermal properties of insulating glass at a fraction of the weight.

[51][16] It also partnered with the MIT Media Lab to assist artists who were creating works involving virtual reality and artificial intelligence.

Artist Lawrence Weiner was commissioned to decorate the plaza with pavers arranged into 12-foot (3.7 m) letters, which would spell the phrase "In front of itself".

[16] The exhibitions and performances announced before the building's April 5, 2019, opening included a concert series exploring the impact of African American music conceived and directed by Steve McQueen and a creative team including Quincy Jones; a collaboration between artist Gerhard Richter and music composers Steve Reich and Arvo Pärt, the eponymous "Reich Richter Pärt'; "Norma Jeane Baker of Troy", a performance piece by the poet Anne Carson with music by Paul Clark, starring Ben Whishaw and Renee Fleming; and an exhibition of work from artist Trisha Donnelly.

[57] During the pandemic, emergency staircases were opened to allow visitors to comply with COVID-19 social distancing regulations by avoiding the elevators.

[58] During early 2021, the Shed announced it would resume live performances with a series featuring Kelsey Lu, the New York Philharmonic, Renée Fleming, and Michelle Wolf in April 2021.

Board members on Manhattan Community Board 4 stated that the Shed "could lack class", that the word "culture" is too vague for the name of such an exhibition space, and that problems could arise when a 20,000 square feet (1,900 m2) space is closed off twice a year for two weeks (adding up to a month annually) for New York Fashion Week.

[67][68][69][70] Community board members also state that when the retractable roof is closed, 20,000 square feet (1,900 m2) of open public space would be lost.

[71] In an editorial for the art website Artsy, one writer stated that although "the building's innovative architecture seems ready to withstand the weight of [the Shed's] grand ambitions", the construction of the Shed also had the unforeseen side effect of "making New York ever less accessible for those without financial means", considering the poor neighborhoods located close to Hudson Yards.

[31] In August 2019, news of Shed board member Stephen Ross's plans to host a fundraiser for U.S. president Donald Trump's 2020 reelection campaign led several artists to protest.