The modeling of plants has a relatively long history, but the modeling of the fundamental relationships between molecular-level regulatory mechanisms, short- and long-distance signaling, and the resulting plant form introduces new challenges and requires new methodologies. Their development is a fascinating area of current interdisciplinary research. In my presentation, I will discuss mathematical models and computer simulations of plants, with a focus on the model plant Arabidopsis thaliana. The objective of these models is the understanding of developmental mechanisms that take place at different levels of plant organization, and the temporal and spatial integration of these mechanisms. Examples include short- and long-distance signaling, spiral phyllotaxis, the fate of buds, and the development of plant architecture. Interactive visual simulations of these processes have been implemented using the formalism of L-systems.