In this paper, a bond-based peridynamic (PD) advection–reaction–diffusion model is formulated to simulate processes involving chemical reactions, flows, and diffusion. In the formulation, the reaction rate, represented by a body force-like local term, depends on the local concentrations of the reactants, and the dependence varies according to the reaction type. Both linear and nonlinear dependencies are considered. A system of coupled PD equations for each substance is solved numerically. We verify and validate the PD advection–reaction–diffusion model by comparing results with those from a corresponding classical model and from experiments in both 1D and 2D, for a bimolecular reaction (A+B→AB) in a flowing aqueous environment, similar to purifying polluted water flowing in a channel, via chemical reactions. The model is also used to simulate bimolecular advection–reaction–diffusion in heterogeneous media with impermeable inclusions, and to simulate polymer degradation through hydrolysis and diffusion, similar to how biodegradable polymer implants dissolve.