The research field of orthogonal polynomials and that of holomorphic dynamics have been living side by side without much interaction for many years. In a joint project with Henrik L. Pedersen Dept. of Math. Copenhagen Univ., Christian Henriksen Compute, Tech. Univ. of Denmark and Jacob S. Christiansen Mat. Lund Univ. we have taken up the task of finding and exploring bridges between the two fields. This has so far resulted in a joint paper, where we prove fundamental relations between the two fields. In projects, underway with Signe E. A. Jensen, North Western Univ. and with Eva Uhre, INM RUC we pursue further relations. In the talk I will provide relevant background explain the main results so far and point to further questions.