Recent evidence has emerged linking coordinated campaigns by state-sponsored actors to manipulate public opinion on the Web. Campaigns revolving around major political events are enacted via mission-focused "trolls." While trolls are involved in spreading disinformation on social media, there is little understanding of how they operate, what type of content they disseminate, how their strategies evolve over time, and how they influence the Web's information ecosystem. In this paper, we begin to address this gap by analyzing 10M posts by 5.5K Twitter and Reddit users identified as Russian and Iranian state-sponsored trolls. We compare the behavior of each group of state-sponsored trolls with a focus on how their strategies change over time, the different campaigns they embark on, and differences between the trolls operated by Russia and Iran. Among other things, we find: 1) that Russian trolls were pro-Trump while Iranian trolls were anti-Trump; 2) evidence that campaigns undertaken by such actors are influenced by real-world events; and 3) that the behavior of such actors is not consistent over time, hence automated detection is not a straightforward task. Using the Hawkes Processes statistical model, we quantify the influence these accounts have on pushing URLs on four social platforms: Twitter, Reddit, 4chan's Politically Incorrect board (/pol/), and Gab. In general, Russian trolls were more influential and efficient in pushing URLs to all the other platforms with the exception of /pol/ where Iranians were more influential. Finally, we release our data and source code to ensure the reproducibility of our results and to encourage other researchers to work on understanding other emerging kinds of state-sponsored troll accounts on Twitter.