Abstract: With the discovery of over 5000 extra-solar planets to date, the formation and evolution of planets and planetary systems are among the most rapidly developing fields of astrophysics. In the standard ‘bottom-up’ scenario, planets form from planetesimals — km or larger-sized bodies. Planetesimals form from small, mm-cm size pebbles, which themselves form from micro-sized dust grains immersed in gaseous protoplanetary disks around young stars. I will describe several obstacles, but also new possibilities, on the road from dust to planets from recent theoretical modeling of planetesimal formation and evolution in modern models of protoplanetary disks.