Abstract Fold-and-thrust (FAT) belts occur worldwide and have long been the focus of research of structural geologists who have devised a variety of techniques to image, characterize and model their main structural features. This introductory chapter reviews the principal geological features of FAT belts formed in different settings, emphasizing aspects related to their kinematic evolution and structural styles. Despite great advances, challenges remain, particularly in the understanding of the spatial and temporal evolution (4D) of FAT belts and their controlling factors. These research efforts are being assisted by the growing availability to researchers of relatively new tools to collect field data, high quality 3D seismic data, and computer and laboratory modelling tools. This volume includes technical papers presented in the conference ‘International Meeting of Young Researchers in Structural Geology and Tectonics (YORSGET-08)’ held in Oviedo (Spain), together with other papers on the same theme. These papers deal with FAT belts in different parts of the world and cover a broad range of different aspects, from detailed structural analysis of single structures to regional issues, and from studies based on classical field structural geology to modelling.