Acyclic preference-based systems recently appeared as an elegant way to model many P2P unstructured or hybrid systems. The strength of these systems is a self-stabilizing property that allows to provide analytical results in addition to empirical validation. In this chapter, we give the keys to understand and use acyclic preference-based. After a brief introduction to the roots and notation of the model, the main convergence theorem is exposed and a description of P2P-relevant preferences is given. Ensues an explanation of the combinatory techniques used to refine the convergence study, and a statistical description, based on mean field assumptions, of the stable configurations of acyclic preference-based systems. For some preferences, we observe that the stable configuration is a small-world.