After 25 years of laboratory research on protoplanetary dust agglomeration, a consistent picture of the various processes that involve colliding dust aggregates has emerged. Besides sticking, bouncing and fragmentation, other effects, like, e.g., erosion or mass transfer, have now been extensively studied. Coagulation simulations consistently show that µm-sized dust grains can grow to mm-to cm-sized aggregates before they encounter the bouncing barrier, whereas sub-µm-sized water-ice particles can directly grow to planetesimal sizes. For siliceous materials, other processes have to be responsible for turning the dust aggregates into planetesimals. In this article, these processes are discussed, the physical properties of the emerging dusty or icy planetesimals are presented and compared to empirical evidence from within and without the Solar System. In conclusion, the formation of planetesimals by a gravitational collapse of dust "pebbles" seems the most likely.