This course provides an in-depth overview of two state-of-the-art graph-based methods for segmenting three-dimensional structures in medical images: graph cuts and the LOGISMOS (Layered Optimal Graph Image Segmentation of Multiple Objects and Surfaces) approach. Such graph-based approaches are becoming increasingly used in the medical image analysis community, in part, due to their ability to efficiently produce globally optimal three-dimensional segmentations in a single pass (not requiring an iterative numerical scheme). Additionally, LOGISMOS enables the simultaneous optimal detection of multiple surfaces in volumetric images, which is important in many medical image segmentation applications. In the first part of the course, we provide a broad overview of both graph cuts and the LOGISMOS approach, including the presentation of a number of example applications. In the second and third parts of the course, we present the algorithmic details of graph cuts and the LOGISMOS approach, respectively. In the final part of the course, we discuss the design of cost functions, which is of paramount importance in any graph-based approach.