Phyllotaxis, the regular arrangement of leaves or flowers around a plant stem, is an example of developmental pattern formation and organogenesis. Phyllotaxis is characterized by the divergence angles between the organs, the most common angle being 137.5 degrees , the golden angle. The quantitative aspects of phyllotaxis have stimulated research at the interface between molecular biology, physics and mathematics. This review documents the rich history of different approaches and conflicting hypotheses, and then focuses on recent molecular work that establishes a novel patterning mechanism based on active transport of the plant hormone auxin. Finally, it shows how computer simulations can help to formulate quantitative models that in turn can be tested by experiment. The accumulation of ever increasing amounts of experimental data makes quantitative modeling of interest for many developmental systems.