Nanometer memories are highly prone to defects due to dense structure, necessitating memory built-in self-repair as a must-have feature to improve yield. Today’s system-on-chips contain memories occupying an area as high as 90% of the chip area. Shrinking technology uses stricter design rules for memories, making them more prone to manufacturing defects. Further, using 3D-stacked memories makes the system vulnerable to newer defects such as those coming from through-silicon-vias (TSV) and micro bumps. The increased memory size is also resulting in an increase in soft errors during system operation. Multiple memory repair techniques based on redundancy and correction codes have been presented to recover from such defects and prevent system failures. This paper reviews recently published memory repair methodologies, including various built-in self-repair (BISR) architectures, repair analysis algorithms, in-system repair, and soft repair handling using error correcting codes (ECC). It provides a classification of these techniques based on method and usage. Finally, it reviews evaluation methods used to determine the effectiveness of the repair algorithms. The paper aims to present a survey of these methodologies and prepare a platform for developing repair methods for upcoming-generation memories.