In the study of molecular and phenotypic evolution, understanding the relative importance of random genetic drift and positive selection as the mechanisms for driving divergences between populations and maintaining polymorphisms within populations has been a central issue. A variety of statistical methods has been developed for detecting natural selection operating at the amino acid and nucleotide sequence levels. These methods may be largely classified into those aimed at detecting recurrent and/or recent/ongoing natural selection by utilizing the divergence and/or polymorphism data. Using these methods, pervasive positive selection has been identified for protein-coding and non-coding sequences in the genomic analysis of some organisms. However, many of these methods have been criticized by using computer simulation and real data analysis to produce excessive false-positives and to be sensitive to various disturbing factors. Importantly, some of these methods have been invalidated experimentally. These facts indicate that many of the statistical methods for detecting natural selection are unreliable. In addition, the signals that have been believed as the evidence for fixations of advantageous mutations due to positive selection may also be interpreted as the evidence for fixations of deleterious mutations due to random genetic drift. The genomic diversity data are rapidly accumulating in various organisms, and detection of natural selection may play a critical role for clarifying the relative role of random genetic drift and positive selection in molecular and phenotypic evolution. It is therefore important to develop reliable statistical methods that are unbiased as well as robust against various disturbing factors, for inferring natural selection.