The goal of the thesis is to develop the capability to model simultaneously the transport and reaction of dissolved and solid constituents in rivers, lakes and coastal waterbodies. The computational modeling of the reactive transport of suspended particles is particularly challenging because particles settle differentially and they are involved in physiocochemical reactions that are often nonlinear and sometimes fast with respect to the fluid turbulence. Examples of such reactions are particle coagulation, precipitation/dissolution, adsorption, and secondary nucleations. The kinetics of coagulation are examined and it is concluded that in the aquatic environment particle number concentration correlations are significant and that particles of size greater than about 0.1 micron tend to collide most often with particles that are much smaller in size, contrary to the theory of Hunt (1982). An improved model for the collision frequency function for turbulent shear is proposed that takes into account the intermittency in the microscale shear rate. Extending the work of Daly (1984), a kinetic model of frazil ice growth is formulated and verified against experimental data. To incorporate fast, nonlinear reaction kinetics into a general transport model, the transport equation for the one-point, joint scalar probability density function (pdf) is employed. Pope's (1981) Monte Carlo technique for solving the pdf transport equation is extended to allow simulation over nonuniform grids. In addition, stochastic algorithms for simulating differential sedimentation and radial diffusion are developed.