Null distributions of permutation tests for two-sample, paired, and block designs are simulated using the R statistical programming language. For each design and type of data, permutation tests are compared with standard normal-theory and nonparametric tests. These examples (often using real data) provide for classroom discussion use of metrics that are appropriate for the data. Simple programs in R are provided and explained briefly. Suggestions are provided for use of permutation tests and R in teaching statistics courses for upper-division and first year graduate students. (Contains 5 figures and 2 tables.)