This article introduces and discusses bot-based collective blocklists (or blockbots) in Twitter, which have been developed by volunteers to combat harassment in the social networking site. Blockbots support the curation of a shared blocklist of accounts, where subscribers to a blockbot will not receive any notifications or messages from those on the blocklist. Blockbots support counterpublic communities, helping people moderate their own experiences of a site. This article provides an introduction and overview of blockbots and the issues that they raise about networked publics and platform governance, extending an intersecting literature on online harassment, platform governance, and the politics of algorithms. Such projects involve a far more reflective, intentional, transparent, collaborative, and decentralized way of using algorithmic systems to respond to issues like harassment. I argue that blockbots are not just technical solutions but social ones as well, a notable exception to common technologically determinist solutions that often push responsibility for issues like harassment to the individual user. Beyond the case of Twitter, blockbots call our attention to collective, bottom-up modes of computationally assisted moderation that can be deployed by counterpublic groups who want to participate in networked publics where hegemonic and exclusionary practices are increasingly prevalent.