Your success as a scientist will in part be measured by the quality of your research publications in high-quality journals and conference proceedings. Of the three classical rhetorical techniques, it is logos, rather than pathos or ethos, which is most commonly associated with scientific publications. In the mathematical sciences the paradigm for publication is to describe the mathematical proofs of propositions in sufficient detail to allow duplication by interested readers. Quality control is achieved by a system of peer review commonly referred to as refereeing. This guide is an attempt to distill the experience of the theoretical computer science community on the subject of refereeing into a convenient form which can be easily distributed to students and other inexperienced referees. Although aimed primarily at theoretical computer scientists, it contains advice which may be relevant to other mathematical sciences. It may also be of some use to new authors who are unfamiliar with the peer review process. However, it must be understood that this is not a guide on how to write papers. Authors who are interested in improving their writing skills can consult the “Further Reading” section. The main part of this guide is divided into nine sections. The first section describes the Editorial process, the role of the referee within it, and some potential benefits of being a good referee. The second expands on the referee’s role in enforcing quality control. The third describes the major categories of research papers. The fourth addresses the difficult subject of ethical behaviour in a referee. The fifth attempts to solve some common dilemmas that new referees may experience. The sixth describes the major categories of referee’s reports. The seventh discusses the referee’s obligation to improve the technical writing of the paper. The eighth describes the correspondence between the Editor and the referee. The ninth contains pointers to further information on the processes of scientific writing, refereeing, and Editing.