May Swenson was born on May 28, 1913, in Logan, Utah, the daughter of Swedish immigrants. (Her father, Dan Swenson, was a professor of mechanical engineering at Utah State University.) Following her graduation from USU in 1934 she took a job as a reporter for the Deseret News. A year later she moved to New York City where she worked in a variety of jobs, including as a stenographer, until she became the editor for New Directions Press in 1959. In 1966 Swenson quit working as an editor in order to devote herself full time to writing. For the remainder of her life she lived in Sea Cliff, New York. She died on December 4, 1989, and was buried in Logan.

Swenson's trademark was her use of complex wordplay in her poems, which frequently took the form of riddles or unusual arrangements of the words on the page. These "iconographs" often were arranged to resemble the shape of the poem's subject. Frequently classified as a nature poet, Swenson received much praise for her descriptions of natural phenomena and her sensory tone. Her chief themes were animal and human behavior, sexuality, death, and the nature of art and perception. Swenson's poetry has often been compared to the writings of Elizabeth Bishop, e.e. cummings, and Gertrude Stein. Over the course of her career, Swenson published seven volumes of poetry (see list below). In addition to her poetry, Swenson also wrote three books of poems for children, a play, three short stories, and a book of translated poems by the Swedish author, Tomas Tranströmer. Several additional volumes of Swenson poetry have been published posthumously.

May Swenson received a wide variety of recognitions and honors during her career, including serving as poet-in-residence at several universities in the United States and Canada during the late 1960s and early 1970s. She was the recipient of Guggenheim, Ford, Rockefeller, and MacArthur fellowships and a National Endowment for the Arts grant. In 1972 she received a medal from the International Poetry Forum for her translation of Tranströmer. Swenson also received the Shelley Memorial Award from the Poetry Society of America, the Bollingen Prize from Yale University, and an Award in Literature from the National Institute of Arts and Letters. She was also elected a member of the latter organization, as well as the Academy of American Poets of which she later served as chancellor. In 1967 she received a Distinguished Service Gold Medal from Utah State University, and in 1987 an honorary doctor of letters.