  Global stability of traveling wavefronts in a periodic spatial-temporal
environment in $n$-dimension ($n\ge 1$) is studied. The wavefront is proved to
be exponentially stable in the form of $ O(e^{-\mu t})$ for some $\mu>0$, when
the wave speed is greater than the critical one, and algebraically stable in
the form of $O(t^{-n/2})$ in the critical case. A new and easy to follow method
is developed. These results are then extended to the case of time-periodic
media. Finally, we illustrate how the stability result can be directly used to
obtain the uniqueness of the wavefront with a given speed.
