Nanoclays still hold a great strength in biomedical nanotechnology applications due to their exceptional properties despite the development of several new nanostructured materials. This article reviews the recent advances in copolymer/clay nanocomposites with a focus on health care applications. In general, the structure of clay comprises aluminosilicate layers separated by a few nanometers. Recently, nanoclay-incorporated copolymers have attracted the interest of both researchers and industry due to their phenomenal properties such as barrier function, stiffness, thermal/flame resistance, superhydrophobicity, biocompatibility, stimuli responsiveness, sustained drug release, resistance to hydrolysis, outstanding dynamic mechanical properties including resilience and low temperature flexibility, excellent hydrolytic stability, and antimicrobial properties. Surface modification of nanoclays provides additional properties due to improved adhesion between the polymer matrix and the nanoclay, high surface free energy, a high degree of intercalation, or exfoliated morphology. The architecture of the copolymer/clay nanocomposites has great impact on biomedical applications, too, by providing various cues especially in drug delivery systems and regenerative medicine.