This special issue looks at inversion tectonics 3 decades after a late 1980s peak in interest that is documented, for instance, by a 1987 Tectonophysics special issue and a 1989 Geol. Soc. London book that soon became classics. Today inversion tectonics is well established as a basic concept, but by far not all aspects of it are well understood. Even the enormous variety of associated structures has probably not been exhaustively described and explained. The kinematics of inversion structures is particularly complex, and their mechanics a matter of debate. The special issue is meant to illustrate the advances made over the past 30 years but also to point out open questions. It has its roots in a session on inversion tectonics at the 2019 EGU General Assembly. Announced contributions already cover many aspects including the importance of inversion concepts in petroleum exploration, the role of plate-wide stress changes and plate rigidity, improved kinematic and timing constraints for well-studied examples, inversion interfering with regional uplift, and inversion of salt-bearing basins. Case studies, often based on high-resolution seismic data, cover diverse areas from Australia to Scandinavia and inversion events from the Paleoproterozoic to the Paleogene. We invite additional contributions dealing with all aspects of inversion tectonics from architecture over kinematics to dynamics and from field- or seismics-based case studies to analogue and numerical simulations, also including responses of depositional systems to active inversion tectonics. The focus will be on "positive inversion", i.e. a change from normal faulting to thrusting or transpression. However, papers on other cases of fault reactivation would also fit our envisaged frame. We particularly welcome new hypotheses challenging common wisdom!