  Dust constitutes only about one percent of the mass of circumstellar disks,
yet it is of crucial importance for the modeling of planet formation, disk
chemistry, radiative transfer and observations. The initial growth of dust from
sub-micron sized grains to planetesimals and also the radial transport of dust
in disks around young stars is the topic of this thesis. Circumstellar dust is
subject to radial drift, vertical settling, turbulent mixing, collisional
growth, fragmentation and erosion.
  We approach this subject from three directions: analytical calculations,
numerical simulations, and comparison to observations. We describe the physical
and numerical concepts that go into a model which is able to simulate the
radial and size evolution of dust in a gas disk which is viscously evolving
over several million years. The resulting dust size distributions are compared
to our analytical predictions and a simple recipe for obtaining steady-state
dust size distributions is derived. With the numerical model at hand, we show
that grain fragmentation can explain the fact that circumstellar disks are
observed to be dust-rich for several million years. Finally, we investigate the
challenges that observations present to the theory of grain evolution, namely
that grains of millimeter sizes are observed at large distances from the star.
We have found that under the assumption that radial drift is ineffective, we
can reproduce some of the observed spectral indices and fluxes. Fainter objects
point towards a reduced dust-to-gas ratio or lower dust opacities.
