Maps have long been used as tools to dispossess the colonised, establish sovereign control over territories and help engineer states. They not only serve as national logos that encourage commitment to a nation, but cartographic representations also inform scientific and engineering knowledge and practices that are crucial for state‐building. With the rise of neoliberalism and the increasing dissemination of open‐source mapping software since the 1980s, however, more and more governmental and non‐governmental organisations and interest groups are designing maps and disseminating geopolitical visions. Controversies over the territorial contours of Israel among Israeli governmental and non‐governmental organisations exemplify how maps can become discursive repertories in political debates over the contours of national territory in a neoliberal mapping environment. Their cartographic claims‐making reveal cartographic mapping genres that are commonly used by map designers who work in politically contentious regions, in which cartography has become a widespread tool to make politics. This paper draws on various conceptual traditions, ranging from the sociology of knowledge, the sociology of religion, sociolinguistics, visual studies and critical cartography in order to identify recurring genres of maps that are used in territorial and geopolitical controversies. The types of maps produced embody different levels of institutional and scientific authority; they possess different substances and designs, and they fulfil varied functions. Given the ever more varied and increasingly user‐defined mapping environment in neoliberal economies, it is important to understand generic map‐types and their use of visual rhetoric in order to persuade a public of certain geopolitical visions.