Granular drainage is a very familiar phenomenon --- the slow flow of sand in an hourglass, corn in a silo... or fuel in a pebble-bed nuclear reactor (our motivation here) --- and yet it presents fundamental theoretical mysteries and experimental challenges. In engineering, the mean flow is commonly described by a ``kinematic'' continuum model, in which the downward velocity satisfies a diffusion equation (with the vertical distance playing the role of time). Litwiniszyn (1963) and Mullins (1972) originally derived this model by assuming that particles move downward as tiny voids make directed random walks upward from the container opening. Taken literally, however, (as has recently been done) this picture predicts mixing rates which are orders of magnitude to too large. Thus we are led to ask: What is the statistical dynamics of particles, consistent with the observed macroscopic flow? In this talk, we discuss particle-tracking experiments using a high-speed digital video camera and a new mathematical model, which suggest that the answer lies in subtle correlations between particle motions.