Abstract: In response to the national significant energy security demands and the dual carbon strategy, large-scale and diversified power electronic equipment is incorporated into the source-grid-load links of the modern power system in different forms and functions. Affected by the multi-timescale time-varying dynamics of diversified power electronic equipment, the stability mechanism of power-electronized power systems (PEPS) has undergone fundamental changes. In recent years, various oscillation accidents with unknown mechanisms related to power electronic equipment have frequently occurred in domestic and foreign power systems, manifesting as multi-timescale time-varying dynamic problems with a wide oscillation frequency range, seriously threatening the safe and stable operation of PEPS. This article starts from the original characteristics of diversified power electronic equipment and summarizes the essential characteristics of PEPS in multi-timescale time-varying dynamics. Then, the different theoretical methods are outlined based on the basic understanding of small-signal modeling and dynamic stability analysis. Subsequently, grounded in the fundamental goal of quickly analyzing and calculating PEPS's multi-timescale time-varying dynamic small-signal stability, this paper condense the research ideas based on small-signal modeling and dynamic stability direct analysis based on linear time-periodic (LTP) theory.