Menus are used for exploring and selecting commands in interactive applications. They are widespread in current systems and used by a large variety of users. As a consequence, they have motivated many studies in Human-Computer Interaction (HCI). Facing the large variety of menus, it is difficult to have a clear understanding of the design possibilities and to ascertain their similarities and differences. In this article, we address a main challenge of menu design: the need to characterize the design space of menus. To do this, we propose a taxonomy of menu properties that structures existing work on visual menus. In order to highlight the impact of the properties on performance, we begin by refining performance through a list of quality criteria and by reviewing existing analytical and empirical methods for quality evaluation. The taxonomy of menu properties is an unavoidable step toward the elaboration of advanced predictive models of menu performance and the optimization of menus. A key point of this work is to focus both on menus and on the properties of menus, to enable a fine-grained analysis in terms of performance.