A Physical Random Function (PUF) is a random function that can only be evaluated with the help of a complex physical system. We introduce Controlled Physical Random Functions (CPUFs) which are PUFs that can only be accessed via an algorithm that is physically bound to the PUF in an inseparable way. CPUFs can be used to establish a shared secret between a physical device and a remote user. We present protocols that make this possible in a secure and flexible way, even in the case of multiple mutually mistrusting parties. Once established, the shared secret can be used to enable a wide range of applications. We describe certified execution, where a certificate is produced that proves that a specific computation was carried out on a specific processor. Certified execution has many benefits, including protection against malicious nodes in distributed computation networks. We also briefly discuss a software licensing application.