Cellular networks are the only means of digital communication for the vast majority of the world's population. Although such systems have traditionally been viewed as secure due to their relatively closed nature, their transition toward an all-IP infrastructure and convergence with the larger Internet creates the potential for new threats to users' security and privacy. This article considers a number of such challenges and discusses why solutions from the current Internet are unlikely to be directly applicable. Successfully addressing these issues is of critical interest to not only telecommunications providers, but also businesses and private citizens worldwide.