Over the last three decades, the numerical simulation of ion trajectories within collision free environments was established as basis for the design of mass analyzers, electrostatic lenses and other ion optical devices. With the advent of atmospheric pressure ionization (API), ions are generated at elevated background gas pressures and in chemically reactive environments. Today, numerical simulations of charged particles have to consider physical and chemical interactions with the background gas. At the same time, the continuously increasing performance of modern computer systems allows to apply computationally demanding numerical models on such simulation problems. In this work, the motion of gas phase ions at atmospheric and intermediate pressure is simulated to investigate the performance, validity and applicability of numerical methods for typical simulation problems in API. Furthermore, new numerical models are developed to simulate the chemical dynamics of charged particles in reactive environments. This work is structured in three sections: First, two established numerical approaches, particle tracing in SIMION with the Statistical Diffusion Simulation (SDS) extension and electrokinetic flow simulation in Comsol Multiphysics, are validated with a benchmark experiment. A bulk gas flow simulation performed in Comsol serves as input for both ion migration models. The SIMION calculation reproduces the experimental result well, while the electrokinetic flow simulation exhibits a significantly lower validity. Second, the ion migration in a complex commercial ion source (MPIS) is simulated with SIMION/SDS. A validated simulation of the complex bulk gas flow, which is required as input, is available from a joint research project. The comprehensive set of SIMION/SDS simulations reproduces the experimental spatially resolved ion signal (DIA) in the ion source very well. This demonstrates that the simulation approach is valid. In contrast, the temporal evolution of the ion signal is not well reproduced by the simulations. Rationales for the discrepancies are discussed and assessed with proof-of-concept calculations. In the third part, Reaction Simulation (RS), a module for the Monte-Carlo simulation of chemical kinetics of ions, is presented. The dynamics of proton bound water clusters are simulated with RS to describe the observed drift of the Reactant Ion Peak in Ion Mobility Spectrometry. Comparison with experimental data validates the simulation results gathered with RS. Furthermore, RS is expanded with a model for the increasing effective ion temperature at elevated electrical fields. With this extension the simulation of high field ion dynamics and chemical kinetics with significant electrical heating of ions is possible with RS, allowing the simulation of ion dynamics in e.g. RF ion guides or ion funnels. The validity of the modified RS module is assessed by comparing simulations of high field devices (e.g., collision cells, differential ion mobility analyzers) with literature data. The simulations performed in this work require the transfer of data from gas dynamics calculations to the ion dynamics models. This is achieved with custom programs which are described in detail. The analysis of raw simulation data and the visualization of the calculation results is also conducted with custom software. Particularly, a web based data browser (DIA explorer) is presented, which visualizes calculated and experimental DIA in a complex multidimensional parameter space. This work demonstrates the feasibility of the developed numerical methods for productive ion dynamics simulations, for example in the domains of instrument design and fundamental research and outlines future development opportunities.