Rapid progress in the CMOS technology for the past 25 years has increased the vulnerability of processors towards faults. Subsequently, focus of computer architects shifted towards designing fault-tolerance methods for processor architectures. Concurrently, chip designers encountered high order challenges for designing fault tolerant processor architectures. For processor cores, redundancy-based fault tolerance methods for fault detection at core level, micro-architectural level ,thread level , and software level are discussed. Similar applicable redundancy-based fault tolerance methods for cache memory, and hardware accelerators are presented in the article. Recent trends in fault tolerant quantum computing and quantum error correction are also discussed. The classification of state-of-the-art techniques is presented in the survey would help the researchers to organize their work on established lines.