Memristor memory has got outstanding characteristics to replace the present memory technologies. The advantages of memristor memories include non-volatility, high density, low power consumption, fast operating speed, and ability to function as multi-level cell. In spite of having numerous advantages, they are highly prone to process variations. Fault analysis shows that there are exclusive faults occur in memristor in addition to other traditional memory faults. Several latest research works are trying to address these issues by different schemes. This paper aims to summarize the recent research progress in terms of memristor faults, fault modeling, testing, and testability schemes. © 2017 Pushpa Publishing House, Allahabad, India.