A prestige journal in the humanities that seems quite aware of its status. But given the academic celebrity of many of its contributors, and its generally forbidding editorial standard (it very rarely publishes grad students), it tends to reflect, and occasionally set, many of the current agendas of (American) humanities research.
The journal is supported at the University of Chicago, from which it draws much, but not all, of its editorial board. It was founded in 1974, a latecomer in the spate of journals founded after “theory”'s introduction to the American academy. Here's editorial board member James Chandler on the journal's reticent engagement with theory:
There was something latent in [CI's] strange unfashionability that gave the journal its chance. I want to describe this as a distinctive kind of attention to the disciplinary system of the cold war university. Not exactly theory—at least not theory in the sense that we have come to associate it with, say, the famous Johns Hopkins symposium on structuralism in 1968. It was something more, well, Aristotelian than that, a methodological self-consciousness about critical practice that might better be described as a sense of where one is in the disciplinary scheme of things—at least in that part of the scheme that pertains to the arts, the humanities, and the interpretive social sciences. (James Chandler, “Critical Disciplinarity”, CI 30.2 (Winter 2004): 355-60)
Ambivalence towards disciplinarity in the wake of 1960s poststructural critiques of the human sciences has always informed CI's sense of itself. It continues to tack closer to the literary uptake of high theory (or at least high seriousness) than cultural studies. Where cultural studies's interdisciplinarity has always been a critique of academic disciplines, direct or implied, CI's focus on a meta-disciplinary idea of the humanities is far less willing to dismiss past scholarship, for better and for worse.
An anniversary issue in 2004 (from which I pulled the above quote) asked many contributors to comment on the project of “critical inquiry” today. Responses varied, but a major preoccupation was the disconnect between theory and politics. The immediate occasion was the beginning of the Iraq invasion, which caused some soul-searching about the (non-)effects of theory. Since then, the journal has published more explicitly political content, especially on the Israeli-Palestinian conflict (translation of an exchange between Blanchot and Levinas; controversy over the Frank Gehry-designed Museum of Tolerance planned for Jerusalem). Incidentally, major theorists's contributions tend to stay within the limits of some narrower idea of politics: Zizek (tolerance, pluralism), Jameson (space flight, Sokurov), Butler (academic freedom) and Nancy Fraser (justice) all apparently shop their more committed Marxist or feminist writings elsewhere.
Other recent directions: science studies and ecology; translations of essays by Jacques Ranciere, Alain Badiou, and Roberto Esposito; interrogating multitude and governmentality; art histories and media materialities; literature and reading, considered within a broader framework of media studies; individual essays on Agamben, Deleuze, Foucault; memorials for Edward Said and Derrida; and, laudably, more writing from social scientists than most other cultural studies journals. University of Chicago anthropologists like Marshall Sahlins, Michael Taussig, and Jean and John Comaroff publish here, bringing a different tradition of thinking about culture to bear.