Concrete is the standard construction material for buildings, bridges, and roads. As safety plays a central role in the design, monitoring, and maintenance of such constructions, it is important to understand the cracking behavior of concrete. Computed tomography captures the microstructure of building materials and allows to study crack initiation and propagation. Manual segmentation of crack surfaces in large 3d images is not feasible. In this paper, automatic crack segmentation methods for 3d images are reviewed and compared. Classical image processing methods (edge detection filters, template matching, minimal path and region growing algorithms) and learning methods (convolutional neural networks, random forests) are considered and tested on semi-synthetic 3d images. Their performance strongly depends on parameter selection which should be adapted to the grayvalue distribution of the images and the geometric properties of the concrete. In general, the learning methods perform best, in particular for thin cracks and low grayvalue contrast.