It is believed that planets are formed by aggregation of dust particles suspended in the turbulent gas forming accretion disks around developing stars. We describe a mechanism, termed 'Stokes trapping', by which turbulence limits the growth of aggregates of dust particles, so that their Stokes number (defined as the ratio of the damping time of the particles to the Kolmogorov dissipation timescale) remains close to unity. We discuss possible mechanisms for avoiding this barrier to further growth. None of these is found to be satisfactory and we introduce a new theory which does not involve the growth of small clusters of dust grains.

30 pages, 4 figures. Revised version has improved concluding remarks, extended discussion of sticking velocity