In the nanoscale era, enhancing the performance of digital circuits and systems becomes increasingly cumbersome. As a result, computing becomes increasingly heavy with multimedia processing. Approximate computing is regarded as one of the emerging technologies that could produce less-than-optimal results which are sufficient enough in user's perspective. This is accomplished by minimizing energy consumption as well as hardware area. The slight compromise in output quality is acceptable for inherent error resilient applications. This paper reviews different types of existing CMOS based approximate circuits designed by various functional approximation techniques. Further, this survey focuses on analyzing the existing approximate arithmetic circuits based on various error metrics such as error rate, error distance, mean error distance, normalized error distance, and minimum acceptable accuracy. The impact of approximation on circuit characteristics for instance, delay, power consumption and throughput are also presented. This paper critically reviews the progress made in the context of approximate computing by using CMOS architecture and its impact on replacing with RRAMs (Memristor). The latter is reportedly found to be energy efficient due to its nano-scale dimension. Although memristor based approximation is still in its infancy, it is high time to understand its emerging importance in nanoscale computing in general and approximate computing in particular. © 2006-2018 Asian Research Publishing Network (ARPN).