Online social spaces have emerged as theaters of information warfare that proceed both separate from and in conjunction with real-world conflict, with influence operations launched by both state- and non-state actors, and targeting both domestic and international audiences. This talk examines methods for characterizing, tracking, and discovering these influence campaigns across online spaces. Using signals from language, information-sharing, and social interaction, we identify potential strategies of Russian manipulation in the US 2016 election, methods for tracking multiple campaigns from several countries over time, and insights about levels of sophistication across campaigns. The talk ends with an overview of our current work in discovering new influence campaigns, characterizing multi-modal signals in these efforts, and potential frameworks for assessing impact of influence campaigns and counter-messaging efforts in online spaces.