Consider a large group of particles falling very slowly together in a viscous fluid. The interesting and important question is to understand how to formulate an effective theory for the sediment. The difficulty is that even though the mixture might be very dilute the interactions between particles are long ranged, with velocities far from a single particle falling off as $r^{-1}$. Recently it has been realized that the assumptions used in presently accepted effective theories imply that the velocity fluctuations of the particles (relative to the mean flow) diverge in an infinite system. On the other hand, several types of experiments (e.g. (Segre, Herboltzheimer and Chaikin, Phys. Rev. Lett. 79, 2574(1997)) have measured finite fluctuations, independent of system size. Through theory, scaling arguments and computer simulations, this talk will explain what is known and not known about this discrepency, and in general about what is the correct effective theory for a sediment.