In this talk, we will explore the baseband of a modern smartphone, discussing the design and the security countermeasures that are implemented. We will then move on and explain how to find memory corruption bugs and exploit them. As a case study, we will explain in details our 2017 Mobile Pwn2Own entry, where we gained RCE (Remote Code Execution) with a 0-day on the baseband of a smartphone, which was among the target of the competition. We exploited successfully the phone remotely over the air without any user interaction and won \$100,000 for this competition target.