Parameterizations between surface meshes and a variety of domains have numerous applications in computer graphics and geometry processing. In recent years numerous methods for parameterizing meshes have been developed, targeting diverse parameter domains and focusing on different parameterization properties. Mesh Parameterization Methods and their Applications reviews the various parameterization methods, summarizing the main ideas of each technique and focusing on the practical aspects of the methods. It also provides examples of the results generated by many of the more popular methods. When several methods address the same parameterization problem, the survey strives to provide an objective comparison between them based on criteria such as parameterization quality, efficiency and robustness. Mesh Parameterization Methods and their Applications provides guidance to researchers and developers when assessing the suitability of different methods for various applications. The authors focus on the practical aspects of the methods available, such as time complexity and robustness. They also provide multiple examples of parameterizations generated using different methods, allowing the reader to visually evaluate and compare the results.