An account of recent theoretical and experimental advances in the field of excitation transport in disordered systems is presented. First the problem of excitation transport among chromophores (donors) randomly distributed in solution is discussed. Picosecond fluorescence mixing experiments demonstrate that the recent nonperturbative theory for this type of system is accurate at all times and concentrations examined. Next we consider systems with two types of chromophores, donors and traps, randomly distributed in solution. Experiments and theory describe the transport and trapping of excitations over the full range of donor and trap concentrations. These ideas and picosecond transient grating experiments are used to explain the mechanism for fluorescence quenching in concentrated dye solutions, which is shown to be due to excitation transport and trapping by dimers of dye molecules. Finally, the problems of excitation transfer among molecules randomly distributed on a lattice (rather than in a solution) is discussed. An accurate nonperturbative theory is employed to calculate transport observables.