Synesth is one of the most comprehensive and flexible tool for tree reconciliation allowing for events on syntenies (i.e. homologous genomic regions containing multiple genes evolving together) including duplications, transfers, fissions, and transient events going through unsampled species. This model allows building histories that explicate the inconsistencies between a synteny tree (i.e. with leaves representing syntenies rather than single genes) and its associated species tree. An inductive characterization of the solution space using different algebras for each granularity (Pareto-optimal histories, Pareto-optimal event count vectors or minimum event cost histories) leads to efficient dynamic programming algorithms. We show how Synesth can be applied to infer evolutionary scenarios for CRISPR-Cas systems. We address the challenge of building a synteny tree and present FullSynesth, a generalization of Synesth rather starting from a set of gene trees. Finally, we show how this field opens the way to many unexplored algorithmic problems.