  Mixing of finite time-homogeneous Markov chains is well understood nowadays,
with a rich set of techniques to estimate their mixing time. In this paper, we
study the mixing time of random walks in dynamic random environments. To that
end, we propose a concept of mixing time for time-inhomogeneous Markov chains.
We then develop techniques to estimate this mixing time by extending the
evolving set method of Morris and Peres (2003). We apply these techniques to
study a random walk on a dynamic Erd\H{o}s-R\'enyi graph, proving that the
mixing time is $O(\log(n))$ when the graph is well above the connectivity
threshold. We also give an almost matching lower bound.
