While working on Replicant, a fully free/libre version of Android, we discovered that the proprietary program running on the applications processor in charge of handling the communication protocol with the modem actually implements a backdoor that lets the modem perform remote file I/O operations on the file system.
Today's phones come with two separate processors: one is a general-purpose applications processor that runs the main operating system, e.g. Android; the other, known as the modem, baseband, or radio, is in charge of communications with the mobile telephony network. This processor always runs a proprietary operating system, and these systems are known to have backdoors that make it possible to remotely convert the modem into a remote spying device. The spying can involve activating the device's microphone, but it could also use the precise GPS location of the device and access the camera, as well as the user data stored on the phone. Moreover, modems are connected most of the time to the operator's network, making the backdoors nearly always accessible.
Read more at the Free Software Foundation blog.