ABSTRACT Some recent developments in stochastic modeling of transport of inert solutes are discussed. Rather than tabulating all that has been done, we focus on some central issues. We explore the attempts to depart from the limited model for dispersion of the mean concentrations toward a complete stochastic description, and continue by evaluating the means for narrowing the ensemble of all physically plausible realizations toward the one which will eventually become a reality. We discuss some scaling issues: starting from the relationship between the scale of the plume and the scale of the heterogeneity, and ending by analyzing the behavior of finite plumes in domains with evolving scales of heterogeneity. We conclude by exploring the issue of the concentration variability. The limitations of the two-moment characterization are evaluated, and we present a method for computing the entire concentration probability distribution function (pdf) as well as some recent ideas on how to use tracer data for Bayesian updating of the concentration moments.