Erbium-doped / erbium-ytterbium co-doped waveguide amplifiers (EDWAs / EYCDWAs) have received much attention as essential components within large-scale functionalized silicon-based optoelectronic (SBO) chips for their remarkable ability to amplify optical signals on-chip at the communication band combined with their potential application across diverse fields. In this review paper, the research progress of EDWAs / EYCDWAs is reviewed comprehensively. In particular, the research advancements concerning amplifiers constructed with diverse host materials is introduced in details and the gain limitations of the waveguide amplifiers are thoroughly analyzed from multiple perspectives, such as host materials and innovative structural designs. Subsequently, the preparation processes of the gain medium and waveguide structure in EDWAs / EYCDWAs are discussed, and their common application scenarios and commercial applications are summarized. In addition, an assesses is carried out on the challenges encountered by EDWAs / EYCDWAs. Finally, a discussion is held on their potential applications and development prospects in the field of SBO chips, with the aspiration of providing valuable references for the development of EDWAs / EYCDWAs.