During his decade-long relationship with the painter John Button in the 1960s, Burton was introduced to the social networks of the art, dance, and theater communities of New York. He came to meet, among others, Edward Albee, Jerome Robbins, Lincoln Kirstein, and Alex Katz. Throughout the 1960s, Burton attempted to be a playwright and librettist, but in 1965 started writing art criticism. In 1966, he began as an editorial associate at Artnews, eventually becoming an editor. He wrote a substantial amount of art criticism in the late 1960s in this role, including the introduction to the pivotal exhibition Live in Your Head: When Attitudes Become Form at the Kunsthalle Berne. Starting in 1969, he began to make performance art, first contributing to the "Street Works" events held in 1969 (and featuring such artists as Vito Acconci and Eduardo Costa). Throughout the 1970s, Burton was known mostly as an art critic and performance artist. In 1972, he showed his Group Behavior Tableaux performance at the Whitney Museum of American Art, and went on to stage other tableaux performances at such venues as the Guggenheim, Documenta, and the Berkeley Art Museum. He began incorporating furniture into his work as early as 1970, and it would grow from being an active participant in his performances to his main area of output. He first realized his sculptures in 1975, culminating in his exhibition at Artists Space in New York, where he showed his Bronze Chair. Through the remaining 1970s, Burton would continue to create performance art pieces and, increasingly, sculpture and public art. It was public art that caught his imagination, and starting in 1979 he began to reconsider his role as an artist by making works of functional furniture-as-sculpture (pragmatic sculpture, he called it) that were meant to be largely anonymous, invisible, and woven into the fabric of the everyday.