This paper surveys recent approaches towards lobbying if interest groups influence the decision of an incumbent government. It describes the two main channels of influence which mainly exist in parallel, namely contribution payments and the transmission of information through lobbying. Recent extensions to the two basic lobbying models are discussed in great detail. Thereafter follows a short overview over current research, which tries to consolidate the two distinct branches of literature into a general lobbying model. The survey concludes with a summary of the main insights and indicates promising directions of further research.