Over the next decade, processor design will encounter a number of challenges. The ongoing miniaturization of semiconductor manufacturing technologies that has enabled the integration of hundreds to thousands of processing cores on a single chip is pushing the limits of physical laws. The fabrication process has also grown more complex and globalized with widespread use of third-party IPs (intellectual properties). This development ecosystem has complicated the security and trust view of processors. Some of the pressing processor architecture design questions are: (1) how to use reconfiguration and redundancy to improve reliability without introducing additional and potentially insecure system states, (2) what analytical models lend themselves best to the joint implementation of reliability and security in these systems, and (3) how to optimally and securely share resources and data among processing elements with high degree of reliability. In this work, we present and discuss (1) principal reliability approaches-error correction code, modular redundancy, (2) processor architecture specific reliability, (3) major secure processor architectures. We also highlight key features of a small representative class of the secure and reliable architectures.