Here we present a selected survey in which we attempt to break down the ever burgeoning literature on inference in the presence of weak instruments into issues of estimation, hypothesis testing and confidence interval construction. Within this literature a variety of different approaches have been adopted and one of the contributions of this survey is to examine some of the links between them. The vehicle that we will use to establish these links will be the small concentration results of Poskitt and Skeels (2007), which can be used to characterize various special cases when instruments are weak. We make no attempt to provide an exhaustive survey of all of the literature related to weak instruments. Contributions along these lines can be found in, inter alia, Stock et al. (2002), Dufour (2003), Hahn and Hausman (2003), and Andrews and Stock (2007), and we view this survey as complementary to those earlier works.