This thesis aims to expand on the fundamental knowledge of crystal growth, selectively focusing on the area of particle-seeded nanowire growth in the III-V materials system. The growth process is complex. It typically occurs via the vapor-liquid-solid method, wherein growth material is supplied in the vapor phase, but the solidification process occurs dynamically, layer by layer, via an intermediary liquid particle. This intermediary phase makes it difficult to assess the correlation between these three phases, and how changes in the vapor phase affect the liquid phase and, in turn, the solidification of the nanowire. This thesis examines the correlation between the vapor, liquid and solid phases, and how the dynamics of the layer-by-layer growth affects the process. This is done in part by combining experimental nanowire growth using metal-organic vapor phase epitaxy with thermodynamic modeling. The main contributions have been in combining thermodynamics, mass transfer and crystal growth kinetics into kinetic Monte Carlo models, and using these models to gain insights into the growth process. The findings of this thesis can be used both to further develop future theoretical models, and to aid in the development of experimental growth, by providing fundamental insights of the growth process and the affects of varying the experimentally accessible process parameters.