Self-assembled buckling patterns of thin films on compliant substrates have been subjected to extensive studies and shown great promise in micro-fabrication. However, most previous studies were limited to planar substrates, and the study of buckling of films on curved substrates has not received sufficient attention. With the constraining effect from various types of substrate curvature, numerous new types of buckling morphologies may emerge which not only enable true three-dimensional (3D) fabrication of microstructures and microdevices but also have important implications for the morphogenesis of quite a few natural and biological systems. We review the scientific aspects of elastic buckling of thin films on several representative curved substrates, emphasizing the critical effect of substrate curvature, its interaction with other material/system parameters, and ways to control the buckles based on mechanical and physical principles and bridge them with prospect applications in biology, biomedical engineering, and small-scale fabrication. © 2013 Springer Science+Business Media New York. All rights are reserved.