Head impacts leading to traumatic brain injury (TBI) present a major health risk today, projected to become the third leading cause of death by 2020. While finite element (FE) models of the human brain are important tools to understand and mitigate TBI, many unresolved issues remain that need to be addressed to improve these models. This work aims to provide readers with background information regarding the current state of research in this field as well as to present recent advancements made possible by improvements to computational resources. Specifically, this has manifested as a drive to introduce more details in FE models in the form of increased spatial resolution and improved material models such as nonlinear and anisotropic constitutive models. The need to work with high-resolution FE meshes is underlined by the dominant wavelengths involved in transient pressure and shear wave propagation and the ability to model the brain surface. We also discuss improvements to experimental validation techniques which allow for better calibrated models. We review these recent developments in detail, highlighting their contributions to the field as well as identifying open issues where more research is needed.