This paper reviews P´olya urn models and their connection to random trees. Basic results are presented, together with proofs that underly the historical evolution of the accompanying thought process. Extensions and generalizations are given according to chronology:
• P´olya-Eggenberger’s urn
• Bernard Friedman’s urn
• Generalized P´olya urns
• Extended urn schemes
• Invertible urn schemes
...
