This paper is written to commemorate the 10th anniversary of academician Ye Duzheng (Yeh T.C.) pass away and his great contributions to the development of atmospheric dynamics. Under the inspiration and guidance of the theory of Rossby wave energy dispersion, remarkable progresses have been made in research on planetary wave dynamics and teleconnections of atmospheric circulation anomalies. This paper aims to make a brief review of the studies on the propagating characteristics of quasi-stationary planetary waves in a three-dimensional spherical atmosphere and the dynamic processes of the interannual and interdecadal variabilities of the East Asian summer and winter monsoon systems. Especially, this paper systematically reviews the progresses of the studies on the impacts of the interannual and interdecadal variabilities of the East Asia/Pacific (EAP) pattern teleconnection wave train propagating along the meridional direction over East Asia and the “Silk Road” pattern teleconnection wave train propagating along the zonal direction within the subtropical jet from West Asia to East Asia on the East Asian summer monsoon system and the summer precipitation variability in China, under the guidance of the theory of Rossby wave energy dispersion. Moreover, this paper reviews the dynamic processes of the impact of the interannual and interdecadal oscillations of the propagating waveguides of boreal quasi-stationary planetary waves on the variability of the East Asian winter monsoon system.