Estimation of species richness of local communities has become an important topic in community ecology and monitoring. Investigators can seldom enumerate all the species present in the area of interest during sampling sessions. If the location of interest is sampled repeatedly within a short time period, the number of new species recorded is typically largest in the initial sample and decreases as sampling proceeds, but new species may be detected if sampling sessions are added. The question is how to estimate the total number of species. The data collected by sampling the area of interest repeatedly can be used to build species-accumulation curves: the cumulative number of species recorded as a function of the number of sampling sessions (which we refer to as ?species-accumulation data?). A classic approach used to compute total species richness is to fit curves to the data on species accumulation with sampling effort. This approach does not rest on direct estimation of the probability of detecting species during sampling sessions and has no underlying basis regarding the sampling process that gave rise to the data. Here we recommend a probabilistic, nonparametric estimator for species richness for use with species-accumulation data. We use estimators of population size that were developed for capture-recapture data, but that can be used to estimate the size of species assemblages using species-accumulation data. Models of detection probability account for the underlying sampling process. They permit variation in detection probability among species. We illustrate this approach using data from the North American Breeding Bird Survey (BBS). We describe other situations where species accumulation data are collected under different designs (e.g., over longer periods of time, or over spatial replicates) and that lend themselves to use of capture-recapture models for estimating the size of the community of interest. We discuss the assumptions and interpretations corresponding to each situation.