Publishing critical essays, commentary, reviews and original artwork by writers and artists such as Ted Berrigan, Alice Notley, and LeRoi Jones, Kulchur was an important vehicle for promoting American poets and cultural critics associated with the New American Poetry of the mid to late twentieth century, particularly the New York School of poets and artists.

The Kulchur Foundation, a non-profit publishing and arts organization, began as a small, literary journal in 1961. The magazine was founded by Marc Schleifer who also edited Kulchur 1 and Kulchur 2 before handing over administrative and editorial control of the magazine to Lita Hornick.

Lita Hornick, who was to become the driving force behind the magazine and Kulchr's subsequent publishing and arts patronage activities, was born Lita Rothbard in 1927 in Newark, New Jersey. She graduated from Barnard College in 1948, where she developed her taste for modern literature and avant-garde poetry. She went on to do graduate work in English at Columbia University, writing her masters thesis on feminist novelist Dorothy Richardson, and, later, her doctoral dissertation on the work of Dylan Thomas. She was married to Morton Hornick and had two sons.

When Hornick took the reigns of the magazine's third issue in 1961 she made significant changes to the publication. The first two issues of the magazine had been managed by Marc Schleifer and published annually--under Hornick's direction the magazine focused more on arts criticism and commentary rather than literary publication and increased its publication schedule to quarterly. Hornick also established Kulchur Press, Inc. as an incorporated business in 1961 (albeit one that never turned a profit and was almost entirely privately funded by her and her husband).

Though Ms. Hornick took over the administrative reigns of the magazine in 1961 with Kulchur 3, she assigned guest editors for the first few issues of the magazine that she published (Gilbert Sorrentino edited Kulchur 5, and Joel Oppenheimer guest-edited Kulchur 6). Starting with Kulchur 7, the magazine was run by Ms. Hornick as managing editor, but supported by an editorial board of LeRoi Jones, Gilbert Sorrentino, Frank O'Hara, Joseph LeSeur, and Bill Berskon. This general arrangement lasted for five issues before Hornick took over the sole editorship of the magazine starting with Kulchur 7 and lasting through the magazine's final issue, Kulchur 20.

The stress and hectic schedule of editing and publishing a quarterly wore on Hornick, so in 1966 she decided to alter the focus of Kulchur, Inc. away from periodicals and cultural commentary and towards publishing books, primarily of poetry. The first book published by Kulchur Press was the contemporary poetry anthology Poems Now, edited by Hettie Jones, though most subsequent books would veer away from the anthology format. Over the course of the Press's run, it published books by notable New York School poets such as Ted Berrigan, John Giorno, and Rochelle Owens, among a host of others. By far the venture's most successful book was Screen Tests, a book of poetry by Gerard Malanga accompanied by photographs of individuals taken by Andy Warhol. Hornick, an avid art collector, was very interested in these collaborations between visual artists and poets, and published a number of such volumes.

In 1970 the name of the organization officially changes from Kulchur Press to Kulchur Foundation to reflect its work as an arts funder and grant-giving agency as well as a publishing venture. This move also allowed the organization to obtain the tax exempt status available to it as a cultural foundation rather than a business. Though Kulchur's publishing efforts remained unchanged with this shift to foundation status, the foundation started to take on more cultural programming than it had previously, such as producing a series of poetry readings at the Museum of Modern Art starting in 1973 and co-producing theatrical productions. In 1981 Kulchur stopped publishing, though Hornick maintained foundation work in the name of Kulchur until her death in 2000.