Formalism, structuralism, and new criticism are all theories of literary criticism. Literary criticism is “the reasoned consideration of literary works and issues” (Encyclopedia Britannica). This is what critics use to determine if a piece of fiction is a work of literary merit. However, literary criticism has changed and evolved throughout history, so there is no single ruling method. Formalism, structuralism, and new criticism all formed in the twentieth century, making them relatively modern schools of literary theory.

Formalism was created in early twentieth century Russia. It wanted to take previous schools of thought and make them more scientific. Formalists believed that the emphasis should be placed on the form—the literary techniques—of the work over the content. They were interested in how works of fiction, especially poetry, could make common language unfamiliar or strange to the reader. The formalists believed that the text should be judged on its own merits without being informed by outside influences.

New criticism gained popularity in mid-twentieth century American thought. It is similar to formalism in that it focuses on the text alone and does not include outside context. However, it differed from formalism in that it also focused on the content of the work in addition to the form. The idea of “close reading” a text for meaning, independent from all other factors, is still dominant today.

Both formalism and structuralism have roots in the linguistic theories of Ferdinand de Saussure, but structuralism is more focused on how language is made up of a system of signs and signification. It arose in the mid-twentieth century and believed that the structure of a work, like its plot and characterization, is part of a universal pattern. From there, critics inferred ideas about both the individual work and the system surrounding it.

Formalism arose in the Soviet Union in the first part of the twentieth century. The key premise of formalism was that literature was not a kind of mirror of reality, but instead a carefully designed linguistic object meant to represent reality in a particular way. It was from this recognition that language and reality are different that led the formalists to concentrate the means by which authors achieved this representation. Some of the main ideas of the formalists included the "alienation effect," or the way literary language makes the world seem "new" or "strange" to readers, and the distinction between "plot" and "story," in which "story" is defined as an actual sequence of events that could have happened, whereas "plot" is the artistic arrangement of those events.

The new critics, like the formalists, were concerned with studying literary language and argued that it was fundamentally distinct from everyday language. The New Critics embraced this idea in radical new ways; they decontextualized literary texts and confined their analysis solely to the words on the page. This kind of "close reading" remains influential in English studies to this day.

Structuralism is a more comprehensive approach to human cognition but has had significant influence on literary studies. Unlike Formalism, Structuralism holds that literary texts must be understood within the context of the various "structures" which shape how humans understand the world. Where the New Critics located meaning within the words of the text, the Structuralists argued that meaning was outside the text, in its relationship to larger "structures" like genre, language, or history.

Formalism, structuralism, and New Criticism are all schools of literary theory, though structuralism is a mode of thought that extends beyond the literary into other disciplines as well. As schools of literary theory, however, each presents their own understandings of what a text is and how it should be read and interpreted.

Philosophically, in a very basic sense, all three forms of literary theory argue that what a text means is contained in the very text itself, what lies on the page before the reader, and that recourse to any "outside" context is unnecessary. Formalism, as per its name, focuses on the formal features of a text—literary techniques like meter, rhyme, and so forth—and disregards questions of history or the biography of the author to interpret the text. Historically, formalism arises in the early twentieth century with the Russian formalists.

Structuralism, which arises later in the century, around the 1960s, draws from anthropological theories of myth and from linguistics. Structuralism extends formalism's aspirations to deal with only the text itself, striving to create an objective study or "science" of literature. Structuralists search for a "literary grammar," for the universal, abstract structures that govern a text's meaning, believing literature to be just one among many forms of verbal communication.

New Criticism was a phenomenon that dominated American literary theory in the middle of the twentieth century. It was formalist in nature. New Critics believed that the only things that counted in the interpretation of a text were the aesthetic factors on the page.

Formalism is a set of theoretical concepts primarily studied by the disciplines of art, literature, and philosophy -- although it has significant operational implications for mathematics as well. The theory, first and foremost, denotes an emphasis on form -- instead of say content/substance, function, milieu or the relationships between them. Criticism of formalism is based on the argument that particular forms cannot be separated from the particular social and historical contexts in which they are situated -- and thus cannot hold as transcendental axioms or rules that determine (or are the overriding essence of) content or function. 

Structuralism is a set of theoretical concepts constituted through the disciplines of sociology, anthropology, linguistics, psychology, literature, economics, and architecture -- as well as philosophy! This theory, although varied in its differential disciplinary uses, is defined by its insistence that the totality of relationships between things is what determines the individual elements - as parts of the whole. Criticism on structuralism is based on the argument that relationships can be mechanistically determined, furthermore the parts, or say individual humans, have no agency outside the structure they are embedded. The criticism of a deterministic logic can also be leveled against formalism, despite the lesser focus on relationships and their modalities.