Natural aquifers usually exhibit complex physical and chemical heterogeneities,which are key factors complicating kinetic processes,such as contaminant transport and transformation,posing a great challenge in the remediation of contaminated groundwater.Aquifer heterogeneity usually leads to a distinct feature,the so-called“anomalous transport”in groundwater,which deviates from the phenomenon described by the classical advection-dispersion equation(ADE)based on Fick\'s Law.Anomalous transport,also known as non-Fickian dispersion or“anomalous dispersion”in a broad sense,can explain the hydrogeological mechanism that leads to the temporally continuous deterioration of water quality and rapid spatial expansion of pollutant plumes.Contaminants enter and then are retained in the low-permeability matrix from the high-permeability zone via molecular diffusion,chemical adsorption,and other mass exchange effects.This process can be reversed when the concentration of pollutants in high-permeability zones is relatively low.The contaminants slowly return to the high-permeability zones through reverse molecular diffusion,resulting in sub-dispersive anomalous transport leading to the chronic gradual deterioration of water quality.Meanwhile,some contaminants are rapidly transported along the interconnected preferential flow paths,resulting in super-dispersive anomalous transport,which leads to the rapid spread of contaminants.Aquifer heterogeneity is also an important factor that constrains the efficacy of groundwater remediation,while the development,application,and evaluation of groundwater remediation technologies are usually based on the Fickian dispersion process predicted by the ADE equation.Comprehensive studies of the impacts of non-Fickian dispersion on contaminant transport and remediation are still needed.This article reviews the non-Fickian dispersion phenomenon caused by the heterogeneity of geological media,summarizes the processes and current understanding of contaminant migration and transformation in highly heterogeneous aquifers,and eval-uates mathematical methods describing the main non-Fickian dispersion features.This critical review also discusses the lim-itations of existing research and outlines potential future research areas to advance the understanding of mechanisms and modeling of non-Fickian dispersion in heterogeneous media.