In this thesis, fluid flow and solute transport in heterogeneous aquifers and particularly in frac-tured rock have been investigated using Lagrangian Stochastic Advective-Reaction (LaSAR) framework. The heterogeneity of the aquifer structure or fracture configuration, as well as the various reaction/retention processes have been considered in the modelling approach. Advection and retention processes are considered to be the dominant transport processes. Monte-Carlo simulation results for transport of nonreactive tracers in 2D generic heterogeneous aquifers indicate that the travel time τ can be well approximated by a lognormal distribution up to a relative high degree of heterogeneity of the aquifers. Comparison between the Monte-Carlo simulation results and the results of first-order approximation reveals that the analytical solutions of the statistical moments of τ are valid only when the variability of the aquifer properties is small. For reactive tracers, Monte-Carlo simulations have been conducted by accounting for spatial variability of both hydraulic conductivity and one sorption parameter simultaneously. The simulation results indicate that the reaction flow path μ is a nonlinear function of distance for shorter distance, linear function for longer distance, and also that μ and τ are well correlated over the considered parameter range. The parameter β, which is purely determined by the flow condi-tions, quantifies the hydrodynamic control of retention processes for transport of tracers in frac-tures. Numerical simulations have been performed to study the statistical properties of the pa-rameter β, travel time τ and flow rate Q in a single heterogeneous fracture and in a sequence of fractures. The results of Monte-Carlo simulations indicate that the parameter β and τ are corre-lated with a power-law relationship β ∼ τm. The correlation between β and the flow rate Q have also been studied and an inverse power-law relationship β ∼ Q-m is proposed. The establishment of these relationships provides a link between the parameter β and measurable parameters τ (or Q). The LaSAR approach has been applied for prediction, evaluation and interpretation of the results of a number of tracer tests (TRUE-1, TRUE Block Scale and TRUE Block Scale Continuation) conducted by SKB at the Äspö site for tracer transport in fractures. The breakthrough curves may be predicted reasonably well, provided that the retention parameters, boundary conditions and hydraulic properties of the domain are given. The evaluation of TRUE tests indicates that the retention occurs mainly in the rim zone on site characterization time scales, while on the per-formance assessment time scale, diffusion and sorption in the unaltered rock matrix are likely to become dominant retention mechanisms. / QC 20100624