As insurgent challengers disrupt parties and party systems across the democratic world, political scientists need to think more systematically about insurgents and the politics they make. In this article, I propose a new framework for understanding electoral insurgents and their systemic impact on politics in two-party systems. Insurgencies vary along dimensions of regime- and party-orientation, and unfold in four distinct patterns: reconstructive, co-optive, reorienting, and reactive. I compare two reconstructive insurgencies in which the structure, rules, and procedures of an existing major party were challenged and reformed during the postwar period: the New Politics movement inside the U.S. Democratic Party and the New Left in the U.K. Labor Party. Given the barriers to third-party success in these party systems, insurgents were successful at transforming parties when they framed their projects as being in line with specific aspects of the postwar political regime at a moment when that order was in crisis. In each case, insurgents had durable effects on party development by institutionalizing a reformist dynamic that has routinely drawn organizational issues into intraparty contests, undermining organizational legitimacy over time. Thinking systematically about the politics that insurgents make offers a new way of understanding the role of movements and entrepreneurs in party development.