Advances in magnetic resonance imaging (MRI) have enabled non-invasive examination of brain structures in unprecedented details. With increasing amount of high resolution MRI data becoming available, we are at a position to make significant clinical contributions. In this chapter, we review the main approaches to shape analysis for brain structures. The purpose of this review is to provide methodological insights for pushing forward shape analysis research, so that we can better benefit from the available high resolution data. We describe in this review point-based, mesh-based, function-based, and medial representations as well as deformetrics. Their respective advantages and disadvantages as well as the implications of increasing resolution and greater sample sizes on these shape analysis approaches are discussed.