We present the results of a systematic numerical investigation of force distributions in granular packings. We find that all the main features of force transmission previously established for two-dimensional systems of hard particles hold in three-dimensional systems and for soft particles, too. In particular, the probability distribution of normal forces falls off exponentially for forces above the mean force. For forces below the mean, this distribution is either a decreasing power law when the system is far from static equilibrium, or nearly uniform at static equilibrium, in agreement with recent experiments. Moreover, we show that the forces below the mean do not contribute to the shear stress. The subnetwork of the contacts carrying a force below the mean thus plays a role similar to a fluid surrounding the solid backbone composed of the contacts carrying a force above the mean. We address the issue of the computation of contact forces in a packing at static equilibrium. We introduce a model with no local simplifying force rules, that allows for an exact computation of contact forces for given granular texture and boundary conditions.