Granta is a British literary magazine
which started as a student publication
Finally it started publishing outside of the Oxford community in 1979. (It has since been called, "The Elvis Costello of literary magazines." -- New Musical Express) It's this version of which I am familiar.
Past writers included Victor Pelevin, Salman Rushdie, Joyce Carol Oates and recently great work by Dani Shapiro and Henk van Woerden.
It specializes in what could be called global literature, pulling together writers from around the world. Granta also includes photographs that have haunting qualities and are often hard to forget. (A recent example is photographer Kent Klich's photo essay on HIV positive children in Romania). Although, personally I think the magazine's strengths are it's travel writing and it's ability to find new British writers. (I believe, but I may be wrong, that they were the first magazine to publish Salman Rushdie.)
The magazine comes in book form (it should, as it costs twelve bucks) every quarter.