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According to the International Technology Roadmap for Semiconductors (ITRS 2001), embedded memories will continue to dominate the increasing system on chips (SoCs) content in the next years, approaching 94% in about 10 years. Therefore the memory yield will have a dramatical impact on the overall defect-per-million (DPM) level, hence on the overall SoC yield. Meeting a high memory yield requires understanding memory designs, modelling their faulty behaviors in the presence of defects, designing adequate tests and diagnosis strategies as well as efficient repair schemes. This paper presents the state of art in memory testing including fault modeling, test design, built-in-self-test (BIST) and built-in-self-repair (BISR). Further research challenges and opportunities are discussed in enabling testing (embedded) memories, which use deep submicron technologies.