To meet the growing demand for communication capacity, new multi-carrier fiber optical communication technology has become the focus of scientific researchers' attention. The paper reviews the development of traditional Orthogonal Frequency Division Multiplexing (OFDM) in the field of fiber optical communication over the past 20 years and summarizes relevant research on Filter Bank Multi Carrier (FBMC) and Universal Filter Multi Carrier (UFMC) in recent years. Since 2016, scholars worldwide have been addressing the drawbacks of OFDM in optical communication, such as high out-of-band leakage, reliance on Cyclic Prefixes (CP), high Peak-to-Average Power Ratio (PAPR) values, and stringent system synchronization requirements. They have initiated research using new multi-carrier systems as a breakthrough point. FBMC optical communication is characterized by minimal sidelobe power and high spectral efficiency, but due to the use of Offset Quadrature Amplitude Modulation (OQAM), the corresponding Digital Signal Processing (DSP) algorithm needs to be redesigned for virtual part interference. UFMC optical communication has a strong tolerance for time synchronization deviation, and it is less sensitive to frequency offsets. Moreover, it can reuse the DSP algorithms of OFDM. However, challenges remain in further suppressing out-of-band power and reducing computational complexity. Finally, based on the current research status, the paper proposes research directions and suggestions for advancing the next-generation fiber optical communication system.