Results of two- and three-dimensional fracture networks simulations are analyzed within a stochastic Lagrangian transport framework. Within this framework, advective transport in the fractures and retention in the host rock are controlled under general conditions by two Lagrangian parameters: the nonreacting travel time and a parameter related to specific surface area available for diffusion. These parameters are observed in the network simulations to closely follow power-law distributions over a wide range. Based on this observation, a model for the distribution of global arrival times is developed that accounts for the effects of matrix diffusion and the observed spatial fluctuations in velocity. The expected value and higher moments of the arrival time are infinite because of the power-law tails. The location of the peak of the arrival time probability density is used as an alternative measure of the characteristic arrival time. This characteristic arrival time increases faster than linearly with travel distance under some conditions, indicating a type of anomalous transport. These numerical results illustrate potential limitations of the classical advection dispersion equation in describing field scale transport in fractured aquifers.