This paper reviews the difficulties associated with being a statistical reviewer for a medical journal. As background, I consider first the use of statistical reviewers by medical journals, medical journals' policies on statistical peer review, and the limited evidence of its effectiveness. The assessment of a manuscript is considered under the headings of design, methods of analysis, presentation and interpretation, with many illustrative examples of the difficulties to be overcome. I emphasize the judgemental nature of many aspects. I suggest how to present and structure the reviewer's report to the editor. Finally, I consider wider issues, including the various other ways in which statisticians can interact with medical journals.