Accurate modeling of contaminant transport and sorption processes in the soil and landfill liners is a prerequisite for realistic model simulations of contaminant fate and transport in the environment. These studies are also important for the remediation of soil and groundwater contamination. Modeling of contaminant transport through soils and landfill liners consists of either solving the direct/forward problem or the inverse problem. In this thesis, an automated time-stepping implicit procedure is developed from the convergence and error studies of explicit and implicit finite-difference solutions for the advection-dispersion transport of contaminants through soil with different sorption mechanisms. This study is further extended for transient through-diffusion (TTD) transport of contaminant in landfills by considering linear sorption mechanism. To validate the numerical solution and also to study the behavior of finite-difference numerical solutions for TTD transport problem, closed-form analytical solution is derived. Further, a new interface condition is proposed based on the finite-volume procedure for stratified soil or landfill liner system. Solvers are developed for the parameter estimation of inverse problem by integrating the developed procedures for the above forward problem with different optimization procedures. Solvers based on Simulated Annealing (SA) and Genetic Algorithm (GA) are developed for TTD transport in the landfill liners and verified with the existing methods of parameter estimation. Novel swarm intelligence based solver is developed for the first time for parameter estimation in contaminant transport inverse problem to overcome some of the limitations of the classical optimization methods and evolutionary methods such as GA. Additionally, the proposed swarm intelligence based algorithms and a new variant is applied to solve ill-posed problem of contaminant source characterization. The presented work in this dissertation can be unswervingly applied for modeling the contaminant transport in laboratory through-diffusion tests and contaminant transport through landfill liners where the transport is usually considered to be one-dimensional and also diffusion-dominated. Similarly, the advection-dispersion transport through laboratory soil columns can also be modeled with the developed, fast, automated, implicit numerical procedure with very good accuracy. The present study can be applied further for contaminant transport through stratified soil/liner system using fast converging numerical algorithms. Finally, the problems of design parameter estimation and source characterization can be handled accurately by the use of developed automated nature-inspired solvers.