We determine the scaling exponents of polymer translocation (PT) through a nanopore by extensive computer simulations of various microscopic models for chain lengths extending up to N=800 in some cases. We focus on the scaling of the average PT time tau approximately Nalpha and the mean-square change of the PT coordinate, <s2(t)> approximately tbeta. We find alpha=1+2nu and beta=2/alpha for unbiased PT in two dimensions (2D) and three dimensions (3D). The relation alphabeta=2 holds for driven PT in 2D, with a crossover from alpha approximately 2nu for short chains to alpha approximately 1+nu for long chains. This crossover is, however, absent in 3D where alpha=1.42+/-0.01 and alphabeta approximately 2.2 for N approximately 40-800.