Nearly five billion people around the world now use social media, and this number continues to grow. One of the primary goals of social media platforms is to capture and monetize human attention. One means by which individuals and groups can capture attention and drive engagement on these platforms is by sharing morally and emotionally evocative content. We review a growing body of research on the interrelationship of social media and morality–as well the consequences for individuals and society. Moral content often goes “viral” on social media, and social media makes moral behavior (such as punishment) less costly. Thus, social media often acts as an accelerant for existing moral dynamics – amplifying outrage, status seeking, and intergroup conflict, while also potentially amplifying more constructive facets of morality, such as social support, pro-sociality, and collective action. We discuss trends, heated debates, and future directions in this emerging literature.