The inevitably first step towards forming planets is the growth from small interstellar-sized dust to larger aggregates. Future observations with ALMA will for the fist time provide detailed information about the size distribution of circumstellar dust and its radial distribution in disks.
In this talk Til will summarize the physics of the size and spacial evolution of dust in protoplanetary disks. The review will cover laboratory experiments of dust collisions, analytical and numerical modeling of grain growth, the implications planet formation, and how these implications can be tested using millimeter observations.