Several issues related to the organic electroluminescent devices are reviewed. Numerical simulation results are presented for the trap-charge limited conduction processes. Several experimental observations are explained based on our simulations. Current-voltage characteristics, band and charge profiles are obtained to elucidate the conduction mechanisms with large trap densities. Recombination strength dependence, doping effects, and the interplay among the free, discrete, and exponential trap charges in single- and double-carrier devices are discussed.