Skeletal curves have an extensive history in digital image analysis. Shape simplification methods compute skeletal curves as a preprocessing step in software packages for digital image analysis. Recent impressive developments in hardware and image analysis software in general allow the exploitation of images at high grid resolutions. The literature offers a large diversity of algorithms that aim at deforming images into topologically equivalent images; the latter ones should represent the shape of complex objects in a simplified form. The book reviews those algorithms. It illustrates the importance of skeletal curves in the process of finding characteristic properties of 3D volume data. (This is illustrated for the example of confocal microscope images of astrocytes in human brain tissue.) Skeletal curves are sensitive to sampling or noise, and applications require the use of corresponding constraints and adjustments of curve analysis procedures. The adaption of concepts from the continuous space into the digital space is often difficult and requires accurate definitions in the digital space, and research about relevant properties and algorithms.