  More than a decade of dedicated experimental work on the collisional physics
of protoplanetary dust has brought us to a point at which the growth of dust
aggregates can - for the first time - be self-consistently and reliably
modelled. In this article, the emergent collision model for protoplanetery dust
aggregates (G\"uttler et al. 2010) as well as the numerical model for the
evolution of dust aggregates in protoplanetary disks (Zsom et al. 2010) are
reviewed. It turns out that, after a brief period of rapid collisional growth
of fluffy dust aggregates to sizes of a few centimeters, the protoplanetary
dust particles are subject to bouncing collisions, in which their porosity is
considerably decreased. The model results also show that low-velocity
fragmentation can reduce the final mass of the dust aggregates but that it does
not trigger a new growth mode as discussed previously. According to the current
stage of our model, the direct formation of kilometer-sized planetesimals by
collisional sticking seems impossible so that collective effects, such as the
streaming instability and the gravitational instability in dust-enhanced
regions of the protoplanetary disk, are the best candidates for the processes
leading to planetesimals.
