New Formalism, or Neo-formalism, was a late-twentieth century development in American poetry that sought to draw fresh attention to traditional forms of verse in terms of meter, rhyme, and stanzaic symmetry.
Disheartened both by the overwhelming popularity of free verse during the Cold War and by the notion that metrical patterns were somehow antithetical to organic truth, New Formalist poets and their advocates rallied behind the traditions, aesthetics, and practices they believed had been all but abandoned by many of their contemporaries.
Though poets like Anthony Hecht, Howard Nemerov, Richard Wilbur, and Mona Van Duyn had continued to explore the possibilities of form during the 1960s and ’70s, they had been schooled by New Critics, including Yvor Winters, John Crowe Ransom, and Allen Tate, who had been outspoken in defense of formalist verse all along. The poets who considered themselves New Formalists in the ’80s and ’90s were drawn to form in response to the free verse standard that was handed to them.
In the preface to the anthology Rebel Angels: 25 Poets of the New Formalism (1996), editors Jarman and David Mason wrote, "It is no surprise that the most significant development in recent American poetry has been a resurgence of meter and rhyme, as well as narrative, among large numbers of young poets, after a period when these essential elements of verse had been suppressed."
Critics of the movement decried neo-formalists for privileging metrical artifice and (sometimes) stylized speech over otherwise more ambitious, visionary, and free forms. Some have gone so far as to call New Formalism patriarchal. Still, others make the case that free verse is no more or less a form than traditional (metrical, rhythmical) verse.
For further reading, consult Gioia's "Notes on the New Formalism" (Hudson Review, 1987) or his book of essays, Can Poetry Matter?: Essays on Poetry and American Culture. Noteworthy criticism of the movement includes Ira Sadoff’s, "Neo-Formalism: A Dangerous Nostalgia," originally published in American Poetry Review in 1990.