A sampling of areas I've worked on:

    interactions with the social sciences: uncovering what language features make an argument convincing, predicting votes from Congressional speeches, non-textual influences on Amazon helpfulness votes, how language echoing reveals power relationships, whether phrasing affects memorability, hedging and framing in discussions of genetically-modified organisms, etc.
    sentiment analyis and opinion mining
    semantics: paraphrasing work as written up by the New York Times, distributional similarity, lexical entailment, etc.
    information retrieval
    grammar formalisms: complexity of parsing (JACM), learning of CFLs