We provide a physically based explanation for the complex macroscopic behavior of dispersion in porous media as a function of Peclet number, Pe, using a pore-scale network model that accurately predicts the experimental dependence of the longitudinal dispersion coefficient, DL, on Pe. The asymptotic dispersion coefficient is only reached after the solute has traveled through a large number of pores at high Pe. This implies that preasymptotic dispersion is the norm, even in experiments in statistically homogeneous media. Interpreting transport as a continuous time random walk, we show that (1) the power law dispersion regime is controlled by the variation in average velocity between throats (the distribution of local Pe), giving DL ~ Peδ with δ = 3 - ¿ ≈ 1.2, where ¿ is an exponent characterizing the distribution of transit times between pores, (2) the crossover to a linear regime DL ~ Pe for Pe > Pecrit ≈ 400 is due to a transition from a diffusion-controlled late time cutoff to transport governed by advective movement, and (3) the transverse dispersion coefficient DT ~ Pe for all Pe $gg$ 1.