The special issue is comprised of 13 invited papers containing original, previously unpublished contributions in the mechanics of inhomogeneous and functionally graded materials. The invited contributors, including Professor Erdogan who has provided with Dr. Ozturk (coauthor) the lead article summarizing the various types of singularities that may be encountered in contact and fracture mechanics, include selected authors of presentations given at the above conference. Some of these contributors are Professor Erdogan’s ex-students and past or present collaborators, while others are distinguished researchers working in this topical area who did not attend the conference. Analytical, computational, experimental, and theoretical aspects of the mechanics of inhomogeneous media in the broad sense, and functionally graded materials, in particular, are covered by the 13 papers. Topics range from the fundamental aspects of crack propagation in graded materials, construction of elasticity solutions for layered anisotropic media, development of novel computational procedures, and specific problems of technological importance involving graded coatings and cover plates to micromechanics-based calculations involving periodically layered media and functionally graded particulate materials. Examination of the contributed articles reveals the need for a multipronged approach in the modeling and simulation of graded and layered materials, and the important role that locally exact analytical solutions may play in the development of new computational procedures.