Mathematical modelling is a commonly used tool for studying the long-term dynamics of weed populations in agriculture. This was reflected in our review by the large number of scientific papers (134 original publications) and the continuing need to gain an overview over this fast developing field (20 previous review papers were found). In this article, we provide a more comprehensive review than earlier seen, striving to include all relevant publications. Thus, we cover models of the population dynamics of 60 weed species in 40 crops. An online, accompanying database provides an indexed bibliography. Despite the large variation in crops, weeds and geography, the models were surprisingly similar in their approach: structured around the weed life cycle, excluding environmental factors and giving little attention to validation or even documentation of model construction. In addition, their application was similar, limited mostly to strategic decision making. We hope that the overview provided by this review will inspire weed modellers and that it will serve as a basis for discussion and as a frame of reference when we proceed to advance the modelling of weed populations to a new level, developing new approaches and tackling new application domains.