Toxic online political discourse has become prevalent, where scholars debate about its impact on 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 this multidimensional distinction using crowd sourcing.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.Our findings align with 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.Warning: The paper contains examples that readers might find offensive.