It is known for decades that computer-based systems cannot be understood without a concept of modularization and decomposition. We suggest a universal, expressive, intuitively attractive composition operator for Petri nets, combined with a refinement concept and an algebraic representation of nets and their composition. Case studies show exemplarily, how large systems can be composed from tiny net snippets. In the future, more field studies are needed to better understand the consequences of the proposed ideas in the real world.