On February 24, 2022, when Vladimir Putin announced Russia's "special military operation" into Ukraine, he claimed that Ukraine was led by "far-right nationalists and neo-Nazis" and that the purpose of Russia's invasion was to "demilitarize and denazify Ukraine." Russian leaders and propagandists have at once denied the existence of a Ukrainian nation and called for purging or cleansing the Ukrainian territory, in terms that often mirror rhetoric preceding past genocides. In this report, the authors seek to shed light on how Russia's extremist, hate-peddling narratives deployed in the war have spread online through social media. Have Russia's propagandists and its extremists been successful in reaching broad audiences through social media? Are their narratives fueling racially or ethnically motivated violent extremism (REMVE) in ways that might raise the risk of actual violence? Who is spreading and amplifying REMVE narratives? To explore these questions, the authors identify major Russian narratives built around REMVE tropes and themes, identify and explore the online communities engaged in this extreme discourse, and characterize the actors whose voices most significantly shape which content is spread and amplified and the audiences the content is likely to reach. They focus on two major social media platforms, X (formerly Twitter) and Telegram, which have emerged as important forums for online discussions and conversations related to the war in Ukraine.