The computer science research community has became increasingly interested in the study of social media due to their pervasiveness in the everyday life of millions of individuals. Methodological questions and technical challenges abound as more and more data from social platforms become available for analysis. This data deluge not only yields the unprecedented opportunity to unravel questions about online individuals' behavior at scale, but also allows to explore the potential perils that the massive adoption of social media brings to our society. These communication channels provide plenty of incentives (both economical and social) and opportunities for abuse. As social media activity became increasingly intertwined with the events in the offline world, individuals and organizations have found ways to exploit these platforms to spread misinformation, to attack and smear others, or to deceive and manipulate. During crises, social media have been effectively used for emergency response, but fear-mongering actions have also triggered mass hysteria and panic. Criminal gangs and terrorist organizations like ISIS adopt social media for propaganda and recruitment. Synthetic activity and social bots have been used to coordinate orchestrated astroturf campaigns, to manipulate political elections and the stock market. The lack of effective content verification systems on many of these platforms, including Twitter and Facebook, rises concerns when younger users become exposed to cyber-bulling, harassment, or hate speech, inducing risks like depression and suicide. This article illustrates some of the recent advances facing these issues and discusses what it remains to be done, including the challenges to address in the future to make social media a more useful and accessible, safer and healthier environment for all users.