Risk matrices are widely used in risk management. They are a regular feature in various risk management standards and guidelines and are also used as formal corporate risk acceptance criteria. It is only recently, however, that scientific publications have appeared that discuss the weaknesses of the risk matrix. The objective of this paper is to explore these weaknesses, and provide recommendations for the use and design of risk matrices. The paper reviews the few relevant publications and adds some observations of its own in order to emphasize existing recommendations and add some suggestions of its own. The recommendations cover a range of issues, among them: the relation between coloring the risk matrix and the definition of risk and major hazard aversion; the qualitative, subjective assessment of likelihood and consequence; the scaling of the discrete likelihood and consequence categories; and the use of corporate risk matrix standards. Finally, it proposes a probability consequence diagram with continuous scales; providing, in some instances, an alternative to the risk matrix.