Lagrangian statistics are explored as a means of describing the transport of solids in a turbulently flowing liquid. The essential feature of the approach is to represent the concentration field as resulting from a distribution of sources of particles. It is argued that this provides a better framework to understand the physics than the Eulerian analysis currently being used. Fully developed concentration fields are calculated, using the assumptions of homogeneous turbulence and plug flow. It is found that the configuration of solids and the suspended load depend primarily on the ratio of the settling velocity to the friction velocity, which is a measure of the relative importance of turbulence and of settling in depositing particles. The analysis emphasizes the need for a better understanding of the mechanism and the rate of entrainment of particles into a turbulently flowing liquid.