The term programmable matter refers to matter which has the ability to change its physical properties (shape, density, moduli, conductivity, optical properties, etc.) in a programmable fashion, based upon user input or autonomous sensing. This has many applications like smart materials, autonomous monitoring and repair, and minimal invasive surgery, so there is a high relevance of this topic to industry and society in general. While programmable matter has just been science fiction more than two decades ago, a large amount of research activities can now be seen in this field in the recent years. Often programmable matter is envisioned, as a very large number of small locally interacting computational particles. We propose the Amoebot model, a new model which builds upon this vision of programmable matter. Inspired by the behavior of amoeba, the Amoebot model offers a versatile framework to model self-organizing particles and facilitates rigorous algorithmic research in the area of programmable matter.