Over the past couple of years, anecdotal evidence has emerged linking coordinated campaigns by state-sponsored actors with efforts to manipulate public opinion on the Web, often around major political events, through dedicated accounts, or "trolls." Although they are often involved in spreading disinformation on social media, there is little understanding of how these trolls operate, what type of content they disseminate, and most importantly their influence on the information ecosystem. In this paper, we shed light on these questions by analyzing 27K tweets posted by 1K Twitter users identified as having ties with Russia's Internet Research Agency and thus likely state-sponsored trolls. We compare their behavior to a random set of Twitter users, finding interesting differences in terms of the content they disseminate, the evolution of their account, as well as their general behavior and use of Twitter. Then, using Hawkes Processes, we quantify the influence that trolls had on the dissemination of news on social platforms like Twitter, Reddit, and 4chan. Overall, our findings indicate that Russian trolls managed to stay active for long periods of time and to reach a substantial number of Twitter users with their tweets. When looking at their ability of spreading news content and making it viral, however, we find that their effect on social platforms was minor, with the significant exception of news published by the Russian state-sponsored news outlet RT (Russia Today).