In 1916 Smoluchowski derived a mean-field model for mass aggregation in order to develop a mathematical theory for coagulation processes. Since Smoluchowski's groundbreaking work his model has been used in a diverse range of applications such as aerosol physics, polymerization, population dynamics, or astrophysics. After reviewing some basic properties of the model I will address the fundamental question of dynamic scaling, that is whether solutions develop a universal self-similar form for large times. This issue is only understood for some exactly solvable cases, while in the general case most questions are still completely open. I will give an overview of the results that have been obtained and the corresponding techniques that have been developed in the last decade.