Controversies may arise when statistical methods are applied to real problems. The reasons vary, but some possible sources are (i) the user fails to appreciate the limitations of the methods and makes claims that are not justified, (ii) researchers disagree on the appropriate statistical methods and, (iii) results of statistical analyses cannot be reproduced. We provide examples of controversies involving all these sources. The references allow readers to explore these examples in more detail. We hope that this article will help readers identify and assess controversies that they encounter in practice.