The classification of ancient solutions of CSF under some geometric conditions is a parabolic version of Liouville-type theorem. We will present that any ancient smooth embedded finite-entropy curve shortening flow is one of the following: a static line, a shrinking circle, a paper clip, a translating grim reaper, or a graphical ancient trombone constructed by Angenent-You. In particular, our result implies that any compact ancient smooth embedded finite-entropy flow is convex. Moreover, any non-compact ancient smooth embedded finite-entropy flow is either a static line or a complete graph over a fixed open interval. This is based on the joint work with Kyeongsu Choi, Dong-Hwi Seo, and Wei-Bo Su.