Foreword Time-reversal symmetry is of fundamental importance to physics but remains to puzzle physicists until the present day. My first step in research concerned the consequences of time-reversal symmetry for dynamical systems, leading me to observe that while recognized as important, time-reversal symmetry had not received the central attention it deserved and as a consequence, the corresponding theory was not always developed to the required level. I was most fortunate to be able to stimulate further research, in particular, through organizing a Workshop on Time-reversal Symmetry in Dynamical Systems at the University of Warwick in 1996 and writing an accompanying survey article with John Roberts.