  Planets are built from planetesimals: solids larger than a kilometer which
grow by colliding pairwise. Planetesimals themselves are unlikely to form by
two-body collisions; sub-km objects have gravitational fields individually too
weak, and electrostatic attraction is too feeble for growth beyond a few cm. We
review the possibility that planetesimals form when self-gravity brings
together vast ensembles of small particles. Even when self-gravity is weak,
aerodynamic processes can accumulate solids relative to gas, paving the way for
gravitational collapse. Particles pile up as they drift radially inward. Gas
turbulence stirs particles, but can also seed collapse by clumping them. While
the feedback of solids on gas triggers vertical shear instabilities that
obstruct self-gravity, this same feedback triggers streaming instabilities that
strongly concentrate particles. Numerical simulations find that solids 10-100
cm in size gravitationally collapse in turbulent disks. We outline areas for
progress, including the possibility that still smaller objects self-gravitate.
