In this study, shear dispersion in double-porosity systems has been investigated. The major focus of this study is determination of dispersion coefficients through development of mathematical models for solute transport in a variety of coupled double-porosity systems by imposing an accurate boundary condition at the interface between a porous medium and a conduit. Theoretical determination of shear dispersions presented in this thesis can be categorized as shear dispersions in: i) a fracture with porous walls, ii) a capillary tube with a porous wall, iii) a rough-walled fracture, iv) a channel with porous walls under the combined effects of pressure-driven and electro-osmotic flows, and v) a capillary tube with a porous wall under the combined effects of pressure-driven and electro-osmotic flows. For determination of the dispersion coefficients, first, a two-dimensional coupled solute transport model is introduced where the interaction between a porous medium and a conduit is handled by imposing the continuity of concentrations and mass fluxes at the interface instead of applying a source/sink term in the governing equations. Second, the Reynolds decomposition technique is used to develop a reduced one-dimensional model for advective-dispersive transport in a conduit with equivalent transport coefficients such as the dispersion coefficient and the effective advection term. Third, the Laplace transform method combined with the Fourier inversion technique is applied to solve the one-dimensional problems and obtain the concentrations in the porous medium and the conduit as well as mass storage in the porous medium. The developed models with the coupled dispersion coefficients serve as new tools to characterize solute transport in double-porosity systems and also can be used for implementation in the existing simulators for better predictions. The developed models for the shear dispersion find applications in solute transport through fractured rocks, fluid flow in hydraulically fractured shale reservoirs, separation of emulsions in microchannel-membrane systems, and electrically assisted chemical species transport in porous microfluidic networks.