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Abstract On the basis of the sampling data from an assemblage, estimation of species richness (observed plus undetected) is statistically difficult especially for highly diverse assemblages with many rare species. Simple counts of species richness in samples typically underestimate and strongly depend on sampling effort and sample completeness. There are two approaches to infer species richness and make fair comparisons among multiple assemblages based on possibly unequal sampling effort and incomplete samples that miss many species. (i) An asymptotic approach: this approach compares the estimated asymptotes of species accumulation curves. It is based on statistical sampling‐theory methods of estimating species richness. Both parametric and nonparametric methods are reviewed. We focus on the nonparametric estimators that are universally valid for all species abundance distributions. (ii) A nonasymptotic approach: this approach compares the estimated species richnesses of standardized samples with a common finite sample size or sample completeness. It is based on the seamless sample‐size‐ and coverage‐based rarefaction and extrapolation sampling curves. This approach aims to compare species richness estimates for equally large or equally complete samples. These two approaches allow researchers to efficiently use all data to make robust and detailed inferences about species richness. Two R packages (SpadeR and iNEXT) are applied to rainforest tree data for illustration.