Abstract: The minimum time required for the system to evolve from the initial state to the target

state is defined as the quantum speed limit time. This concept can be used to estimate the maximum

rate of evolution from a given quantum state to a desired target state. Here，the development of

quantum speed limit time from closed system to open system is reviewed，and the influence of

non-Markovian environment on the quantum speed limit time of open system is discussed. We hope

that our review is helpful for the future study of the quantum speed limit time.

Key words: quantum speed limit time for closed system, open system quantum speed limit time, quantum in- formation