The thesis presents a modeling framework for simulating three dimensional effects in lithium-ion batteries. This is particularly important for understanding the performance of large scale batteries used under high power conditions such as in hybrid electric vehicle applications. While 1D approximations may be sufficient for the smaller scale batteries used in cell phones and laptops, they are severely limited when scaled up to larger batteries, where significant 3D gradients can develop in concentration, current, temperature, and voltage. Understanding these 3D effects is critical for designing lithium-ion batteries for improved safety and long term durability, as well as for conducting effective design optimization studies. The model couples an electrochemical battery model with a thermal model to understand how thermal effects will influence electrochemical behavior and to determine temperature distributions throughout the battery. Several modeling example results are presented including thermal influences on current distribution, design optimization of current collector thickness and current collector tab placement, and investigation of lithium plating risk in three dimensions. / text