Toxic online political discourse has become prevalent, where scholars debate about its impact to Democratic processes. This work presents a large-scale study of political incivility on Twitter. In line with theories of political communication, we differentiate between harsh ‘impolite’ style and intolerant substance. We present a dataset of 13K political tweets in the U.S. context, which we collected and labeled by those categories using crowd sourcing. Our dataset and results shed light on hostile political discourse focused on partisan conflicts in the U.S. The evaluation of state-of-the-art classifiers illustrates the challenges involved in political incivility detection, which often requires high-level semantic and social understanding. Nevertheless, performing incivility detection at scale, we are able to characterise its distribution across individual users and geopolitical regions, where our findings align and extend existing theories of political communication. In particular, we find that roughly 80% of the uncivil tweets are authored by 20% of the users, where users who are politically engaged are more inclined to use uncivil language. We further find that political incivility exhibits network homophily, and that incivility is more prominent in highly competitive geopolitical regions. Our results apply to both uncivil style and substance.