Estimating abundance has been of interest for many years, in a wide range of areas. An early example was undertaken by Laplace in 1802, and involved estimating the population of France; see Pollock (1991). Early modelling work is well described by Seber (1982), Amstrup et al. (2005, Chapters 2 and 4) and Williams et al. (2002, Chapter 14). Current research involves medical, epidemiological and sociological, as well as ecological and other applications. In this chapter our primary focus is on ecological applications, where similar approaches apply to estimating the abundance of individuals of a particular species as well as the total number of species present in an area. However as we shall see, there are major diﬀerences in models for diﬀerent applications. Statistical methods include parametric and non-parametric alternatives, and often provide analyses of data from marked individuals. Link (2003) has shown how diﬀerent models for abundance estimation can fit data equally well but diﬀer in the estimates of population size that they produce. Thus uncritical use of single models should be avoided. Early research for just two sampling occasions resulted in the Lincoln-Petersen estimate; see Petersen (1894) and Lincoln (1930). For ecological applications models are frequently fitted to data resulting from several capture occasions; however, for studies of human populations, instead of multiple occasions the data may correspond to multiple lists, or multiple observations on a single list.