In this talk, we first discuss how to classify ancient mean curvature flows which converge to a shrinker after rescaling as time goes back. The linearized operator of the flow over a shrinker has finitely many unstable eigenfunctions, and they provide corresponding ancient flows. Next, if time permits, we will consider the ancient flows corresponding to the first eigenfunction and study their nice properties. Then, we will talk about how to use those properties to establish the avoidance theory of unstable singularities.