We describe the design goals and architecture of the Mesquite toolkit, a stand-alone library consisting of state-of-the- art algorithms for mesh quality improvement. The primary considerations in Mesquite design are to ensure that it is comprehensive, effective, efficient, and extensible. We give an overview of the Mesquite architecture and highlight the core classes, their inter-relations, and functionality. We describe the interfaces developed to obtain information from the mesh and geometry and to provide user-control of the quality metrics, algorithms, and termination criterion. Smoothing results for several meshes with a broad range of characteristics are given which showcase Mesquite's versatility.