The 16 chapters presented in this memoir cover some of the recent advances made in the descriptions and analysis of thrust-related fold systems. The chapters include kinematic and geometric analyses of fault-propagation folding, trishear folding, detachment folding, wedge-thrust fold systems, and basement-involved thrust systems. Examples are given from the Zagros fold belt of Iran; the sub-Andean fold belt of western Argentina; the frontal fold belt of the Tianshan, northern margin of the Tarim Basin in western China; from the fold and thrust belts of the Spanish Pyrenees, Taiwan, Wyoming, and southern California; as well as the deep-water fold belts of offshore Brazil and the Niger Delta. In particular, several chapters focus on new analyses of detachment folding as well as improved kinematic and geometric models of thrust-related folding. Improved seismic imaging combined with theoretical, numerical, and analog modeling, plus the detailed field studies as presented in this volume, indicates the range of challenges and the strategies that can be brought to bear in integrating the well-established geometric and kinematic models of thrust fault-related folding with mechanical models to account for the natural complexities of real-world structures. I hope that the readers of this memoir will find these new ideas and concepts relevant for the exploration and exploitation of hydrocarbon systems in fold and thrust belts worldwide.