The fractional quantum Hall effect (FQHE) occurs at a certain magnetic field strengths B*(n) in a two-dimensional electron gas of density n at strong magnetic fields perpendicular to the plane of the electron gas. At these magnetic fields strengths, the system is incompressible, i.e., there is a finite cost in energy for creating charge density fluctuations in the bulk, while the boundary of the electron gas has gapless modes of density waves. The bulk energy gap arises because of the strong electron-electron interactions. While there are very good models for infinite homogeneous systems and for the gapless excitations of the boundary of the electron gas, computational methods to accurately model finite, inhomogeneous systems with more than about 10 electrons have not been available until very recently. We will here review an ensemble density functional approach to studying the ground state of large inhomogeneous spin-polarized FQHE systems. (C) 1996 John Wiley & Sons, Inc.