In this piece, which frames the special issue, “The State of Google Critique and Intervention,” we provide an overview of research focusing on Google as an object of critical study, fleshing out the European interventions that actively attempt to address its dominance. The article begins by mapping out key areas of articulating a Google critique, from the initial focus on ranking and profiling to the subsequent scrutiny of user exploitation and competitive imbalance. As such, it situates the contributions to this special issue concerning search engine bias and discrimination, the ethics of Google Autocomplete, Google's content moderation, the commodification of engine audiences and the political economy of technical systems in a broader history of Google criticism. It then proceeds to contextualize the European developments that put forward alternatives and draws attention to legislative efforts to curb the influence of big tech. We conclude by identifying a few avenues for continued critical study, such as Google's infrastructural bundling of generative artificial intelligence with existing products, to emphasize the importance of intervention in the future.