In this talk, I will first recall some classical results on the existence of traveling waves connecting two stable
steady states for typical reaction-diffusion equations and their analogues. Such an existence result is then
established for a class of bistable evolution systems in homogeneous/periodic environment from a monotone
dynamical system point of view. Finally, the obtained results are illustrated with concrete models that may arise
from population ecology. This talk is based on a joint work with Xiaoqiang Zhao.