Armed non-state actors frequently intervene in democratic politics, producing waves of political violence against voters, candidates, and elected officials. How do we understand these interventions? In democracies, the power to enact a political agenda, channel rents, and punish opponents is vested in legislative and executive institutions. Armed challengers who wish to discredit the state’s political project or enact their own thus face powerful incentives to displace or capture those institutions. How they choose to intervene in the democratic process is, I argue, a function of two variables: how compatible the group's goals are with the democratic process, and how much coercive power the group can bring to bear against voters and elected officials. The combinations of these variables generate a set of four ideal-typical strategies, each of which prescribes a distinct course of violent and nonviolent behavior. Violent organizations with democracy-compatible goals seek to capture democratic institutions. Where they have the coercive wherewithal to demand compliance from voters and elected officials, they appropriate legislative and policymaking processes to fit their political aims; where they do not, they offer corrupt agreements to sympathetic politicians. Armed groups with democracy-incompatible goals instead use violence to discredit and delegitimize democracy, impeding elections through terrorism and, when they enjoy coercive dominance, evicting elected officials and uprooting the democratic state altogether. Groups with a mixture of compatible and incompatible goals attempt to square this circle by publicly attacking high-profile democratic institutions while quietly colluding with local authorities to implement their political agenda. I evaluate these predictions against quantitative, computational, and archival evidence from Latin America. I first examine a low-compatibility armed actor in Sendero Luminoso, a Peruvian Maoist insurgent group. In communities it dominated, Sendero Luminoso impeded elections, evicted local elected leaders, and replaced municipal governments with revolutionary popular councils. These interventions had lasting effects on public trust and participation in democracy. I then turn to a medium-compatibility organization in the Revolutionary Armed Forces of Colombia (FARC). The FARC railed against Colombian democracy but also sought to influence it from within, quietly coercing mayors and seizing state bureaucracies. A final case study turns to a set of democracy-compatible Mexican criminal organizations. These groups secured the cooperation of national politicians through bribery and threatened vulnerable local politicians with violence. These interventions paid off: capture of local governments led to increased rates of extortion and theft from public coffers. These results have important implications for theories of political violence and democratic politics. They provide an explanation for a widespread but little-theorized form of violence: that enacted by armed actors against mayors, legislators, and other elected officials. They also propose a new means of state-building for aspiring political authorities, showing that these groups can appropriate state institutions rather than construct their own. For analysts of democratic politics, they suggest that models of democracy that ignore the influence of coercive actors often miss a key shaper of policy outcomes and an important threat to public faith in democracy. Finally, they underscore the vital importance of accounting for ideological commitments in models of contentious politics.