In this paper we give a presentation about the development of seismic dynamic stress triggering on three aspects:the Coulomb failure stress and theory of seismic dynamic stress triggering,the observational facts and research status,and the problems in research and prospect about seismic dynamic stress triggering. Especially,we make a detailed discussion on the following questions:the triggering effects of seismic dynamic Coulomb failure stress changes on aftershocks,the triggering effects on following remote independent events,the triggering effects of different earthquake types,the triggering effects of volcanoes(mud volcanoes),the triggering relationships between different subevents,and the time delay of seismic dynamic stress triggering. Our results suggest that dynamic stress triggering theory is good in explaining the distribution of aftershocks,triggering remote events and volcanos. We also find that dynamic stress triggering may be affected by the types and directions of faults' rupture,the triggering relationships between different subevents is significant for studying the source of earthquakes,and there is ubiquity of time delay in dynamic stress triggering.