Every mobile phone runs two operating systems; the one you interact with (like Android or Ios), and the one that controls the radio hardware. This second OS is ancient, creaking, and wildly insecure. Security researcher Ralf-Philipp Weinmann of the University of Luxembourg presented work on reverse-engineering the most popular "baseband" OSes from Qualcomm and Infineon and the horrifying security vulnerabilities he found. Anyone operating a cellular base-station (you can buy 'em on Ebay or build them from open source hardware specs) can send a 73-byte message that lets them run raw code on the processor; can silently activate auto-answer, crash the device, brick devices, install rootkits, send SMSes to premium numbers, and more.
You can do some crazy things with these exploits. For instance, you can turn on auto-answer, using the Hayes command set. This is a command language for modems designed in 1981, and it still works on modern baseband processors found in smartphones today (!). The auto-answer can be made silent and invisible, too.
While we can sort-of assume that the base stations in cell towers operated by large carriers are "safe", the fact of the matter is that base stations are becoming a lot cheaper, and are being sold on eBay - and there are even open source base station software packages. Such base stations can be used to target phones. Put a compromised base station in a crowded area - or even a financial district or some other sensitive area - and you can remotely turn on microphones, cameras, place rootkits, place calls/send SMS messages to expensive numbers, and so on. Yes, you can even brick phones permanently.
* The second operating system hiding in every mobile phone [Thom Holwerda/OS News]