We will discuss the application of projective Fraïssé theory to finite rooted trees. By focusing on specific classes of epimorphisms between these structures, we construct projective Fraïssé limits that lead to interesting continua, including the Mohler-Nikiel universal dendroid, the Wa?ewski dendrite, and a new continuum that has yet to be fully characterized. We also introduce the present partial result of the Ramsey property of classes, which, through the Kechris-Pestov-Todorcevic (KPT) correspondence, relates to topological dynamics properties and allow us to calculate the universal minimal flows of automorphism groups of continua. This talk is based on joint work with W. Charatonik, A. Kwiatkowska, and R. Roe.