The origin of planetesimals, roughly kilometer-sized solids, is a long-standing dilemma for planet formation models. The surface gravity of planetesimals promotes growth into terrestrial planets and giant planet cores. Smaller bodies stick much less readily (though small dust grains have sufficient surface area for van der Waals sticking) and are strongly influenced by aerodynamic coupling to gas. The growth of planetesimals might proceed by the gravitational collapse of overdense regions of smaller solids. It was long thought that even weak disk turbulence would stir particles and prevent this gravitational collapse. Recent progress in the dynamics of solid particles in circumstellar gas disks which shows otherwise. In many cases, turbulence can generate particle overdensities. The feedback of particles on gas dynamics (often thought to be a negligible correction) promotes this clumping, by a mechanism called the streaming instability (Youdin & Goodman, 2005; Youdin & Johansen, 2007; Johansen & Youdin, 2007). Recent numerical simulations (Johansen, Oishi, MacLow, Klahr, Henning & Youdin, Nature, 2007) show that self-gravity induces collapse of these clumps toward planetesimals. I will discuss the implications of these results, and avenues for future progress.