Some researchers have argued for the use of or have attempted to make use of randomization tests in single-subject research. To address this tide of interest, the authors of this article describe randomization tests, discuss the theoretical rationale for applying them to single-subject research, and provide an overview of the methodological research into the Type I error rates and statistical power of randomization tests in single-subject designs. It is found that randomization tests generally are an awkward fit to single-subject designs, and they are found to have low statistical power in single-subject contexts. It is therefore recommended that single-subject researchers make sparing, if any, use of randomization tests to analyze their data. (Contains 1 table.)