Organic bulk heterojunction solar cells are often regarded as near-equilibrium devices, whose kinetics are set by well-defined charge carrier mobilities, and relaxation in the density of states is commonly ignored or included purely phenomenologically. Here, the motion of photocreated charges is studied experimentally with picosecond time resolution by a combination of time-resolved optical probing of electric field and photocurrent measurements, and the data are used to define parameters for kinetic Monte Carlo modelling. The results show that charge carrier motion in a prototypical polymer:fullerene solar cell under operational conditions is orders of magnitude faster than would be expected on the basis of corresponding near-equilibrium mobilities, and is extremely dispersive. There is no unique mobility. The distribution of extraction times of photocreated charges in operating organic solar cells can be experimentally determined from the charge collection transients measured under pulsed excitation. Finally, a remarkable distribution of the photocurrent over energy is found, in which the most relaxed charge carriers in fact counteract the net photocurrent.