This paper considers the technologies needed to support the creation of adaptively constructed meshes for general curved three-dimensional domains and outlines one set of solutions for providing them. A brief review of an effective way to integrate mesh generation/adaptation with CAD geometries is given. A set of procedures that support general h-adaptive refinement based on a mesh metric field is given. This is followed by examples that demonstrate the ability of the procedures to adaptively construct anisotropic meshes for flow problems. A procedure for the generation of strongly graded, curved meshes as needed for effective hp-adaptive simulations is also given. (C) 2004 IMACS. Published by Elsevier B.V. All rights reserved.