The dynamic performance of polymer electrolyte membrane fuel cells (PEMFCs) is of great interest for mobile applications such as in automobiles. However, the length scale of a PEM fuel cell's main components are ranging from the micro over the meso to the macro level, and the time scales of various transport processes range from milliseconds up to a few hours. This combination of various spatial and temporal scales makes it extremely challenging to conduct in-situ measurements or other observations through experimental means. Thus, numerical simulation becomes a very important tool to help understand the underlying electrochemical dynamics and transient transport phenomena within PEM fuel cells. In this thesis research, a comprehensive 3D model is developed which accounts for the following transient transport mechanisms: the non-equilibrium phase transfer between the liquid water and water vapor, the non-equilibrium membrane water sorption/desorption, liquid water transport in the porous backing layer, membrane hydration/dehydration, gas diffusion in the porous backing layer, the convective gas flow in the gas channel, and heat transfer. Furthermore, some of the conventionally used modeling assumptions and approaches have been incorporated into the current model. Depending on the modeling purposes, the resulting model can be readily switched between steady and unsteady, isothermal and non-isothermal, single- and multi- phases, equilibrium and non-equilibrium membrane sorption/desorption, and three water production assumptions. The governing equations which mathematically describe these transport processes, are discretized and solved using a finite-volume based commercial software, Fluent, with its user coding ability. To handle the significant non-linearity stemming from the multi-water phase transport, a set of numerical under-relaxation techniques is developed using the programming language C. The model is validated with experimental results and good agreements are achieved. Subsequently, using this validated model numerical studies have been carried out to probe various transient transport phenomena within PEM fuel cells and the cell dynamic responses with respect to different operating condition changes. Furthermore, the impact of flow-field design on the cell performance is also investigated with the three most common flow channel designs.