Critical assemblies of precisely known materials and reproducible and easily calculated geometries have been constructed at the Los Alamos National Laboratory since the 1940s. Initially, these assemblies were built to provide information necessary for the nuclear weapons development effort. Subsequently, intensive studies of the assemblies themselves were undertaken to provide a better understanding of the physics of the fission process and other nuclear reactions in the nuclear materials from which these machine were constructed and in other materials irradiated in these assemblies. Some of these assemblies (notably Jezebel, Flattop, Big Ten, and Godiva) have been used as benchmark assemblies to compare the results of experimental measurements and computations of certain nuclear reaction parameters. These comparisons are used to validate both the input nuclear data and the computational methods. In addition to these normally fueled benchmark assemblies, other assembly machines are fueled periodically to provide specific and detailed results for parameter sensitivity studies for a large number of applications. Some of these machines and their applications are described.