Species richness is the simplest way to describe community and regional diversity (Magurran 1988), and this variable – number of species – forms the basis of many ecological models of community structure (MacArthur & Wilson 1967; Connell 1978; Stevens 1989). Quantifying species richness is important, not only for basic comparisons among sites, but also for addressing the saturation of local communities colonized from regional source pools (Cornell 1999). Maximizing species richness is often an explicit or implicit goal of conservation studies (May 1988), and current and background rates of species extinction are calibrated against patterns of species richness (Simberloff 1986). Therefore, it is important to examine how ecologists have quantified this fundamental measure of biodiversity and to highlight some recurrent pitfalls. Even the most recent reviews of biodiversity assessment (Lawton et al. 1998; Gaston 2000; Purvis & Hector 2000) have not discussed the sampling issues we address in this review in relation to the measurement and comparison of species richness. In contrast, the uses and abuses of species diversity indices, which, by design, combine richness with relative abundance, enjoy a substantial and venerable literature (e.g. Washington 1984), and are thus beyond the scope of this review. We begin by placing several concepts of diverse origin in a common conceptual framework.