Addition of a small percent of clay to polymers improves their stiffness, strength, dimensional stability, and thermal, optical, and barrier properties. Improvements are often attributed to the availability of large numbers of clay nanolayers with tremendous interfacial area. Despite the positive effects from the addition of clay, there are unresolved issues, such as embrittlement, thermal stability, flame retardancy, scratch–wear response of the resultant nanocomposites, and/or achieving a balance between different mechanical and physical properties. In this review, we discuss these issues and the approaches that have been adopted in the expectation of resolving and understanding them, with particular emphasis on our recent and current research.