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In order to meet the increasing bandwidth demand, the future high speed, high capacity and low cost optical short and medium reach Direct Detection (DD) system becomes an inevitable trend. This paper first comprehensively reviews the advanced spectral efficient modulation formats in flexible transceiver and modulation methods which include the Double Side Band (DSB) and Single Side Band (SSB) methods to different transmission scenarios. In addition, considering the issue of different physical layer impairments, the details of the equalization schemes are reviewed. Finally, the extensions of future technology in the short and medium reach DD system are provided.