Mesquite is a linkable software library that applies a variety of node-movement algorithms to improve the quality and/or adapt a given mesh. Mesquite uses advanced smoothing and optimization to untangle meshes, provide local size control, improve angles, orthogonality, skew, and smoothness. Mesquite improves surface or volume meshes which are structured, unstructured, hybrid, or non-conformal. Various element types are permitted. Mesquite is designed to be as efficient as possible so that large meshes can be improved. Mesquite has scaled to 125K cores with 90% efficiency. Mesquite has been used in a wide variety of application settings, including improving initial meshes for PDE simulation in complex geometry, ALE rezoning, boundary layers, and mesh smoothing, using r-adaptivity using error estimates.