We first need to define what traditional literary criticism is. Usually, this refers to the interpretative methodologies practiced prior to the rise of post-structuralism, which began in the 1960s and gained steam in the later 1970s and early 1980s.
The three powerhouses of traditional literary criticism are source studies, biographical criticism, and then, starting in the 1930s, what was called New Criticism.
Source studies are where literary criticism started. As the name indicates, this form of criticism focuses on uncovering what sources were used in a particular piece of literature. This was important for studying the writing of an earlier era, such as the Middle Ages or the Renaissance, when literature borrowed very heavily from earlier works. For example, we know that the Roman poet Ovid was a source for both Chaucer and Shakespeare. The advantage of this kind of criticism is that we can learn a good deal about an author and his intentions by how and why he altered his sources. The limitation is that too much focus on sources can divert attention away from a work's originality.
Biographical criticism was also the bread and butter of literary criticism up until the 1930s. It focused on understanding a literary work in the context of an author's life. Its advantage is that knowing what was going on in a writer's life can help us understand a work of literature and identify who certain characters might be modeled on. However, it has also gone to ludicrous extremes, such as in the assertion that Emily Brontë must have had a secret lover like Heathcliff in order to write Wuthering Heights. This again has the disadvantage of diminishing the role of imagination in the process of literary creation. It also encourages over-reliance on what an author might have said their work is about: writers often transcend their own conscious intentions, and to rely solely on a writer's thoughts can be limiting.
New Criticism was a reaction to the limits of biographical and source study criticism, both of which went outside of the text to understand it. New Critics wanted to first focus on what the text at hand could tell us before jumping to outside studies. This is the backbone of criticism to this day, and may involve such questions as the following: What is the plot, theme, characterization, setting, and tone of a work of literature? Who is telling the story? What kind of language is being used? The advantage of New Criticism is that it encourages close readings of a what a text is actually saying and how it is saying it. The disadvantage is that it leaves out the social and political context in which a work was composed. For example, canonical literature—that is, literature chosen as exemplary of the greatest literature in a culture—began to come under attack in the 1960s and 1970s as reflecting almost entirely the point of view of privileged white males and was often only interpreted from that point of view. This was increasingly seen as far too narrow a view of literature and literary interpretation.