In classical mechanics, matter and fields are completely separated; matter interacts with fields. For particle physicists this is not the case; both matter and fields are represented by particles. Fundamental interactions are mediated by particles exchanged between matter particles. In this article we explain why particle physicists believe in such a picture, introducing the technique of Feynman diagrams starting from very basic and popular analogies with classical mechanics and making the physics of elementary particles comprehensible even to high school students, the only prerequisite being a knowledge of the conservation of mechanical energy. (Contains 6 figures.)