TheRossi X‐ray Timing Explorer(RXTE) is an immensely successful mission of exploration and discovery. It has discovered a wealth of rapid X‐ray variability phenomena that can be used to address fundamental questions concerning the properties of dense matter and strong gravitational fields as well as important astrophysical questions. It has answered many questions and is likely to answer many more, but to follow up fully on the major discoveriesRXTEhas made will require a new X‐ray timing mission with greater capabilities. This introduction to the present volume describes briefly the advantages of X‐ray timing measurements for determining the properties of dense matter and strong gravitational fields, indicates some of the key scientific questions that can be addressed using X‐ray timing, and summarizes selected achievements of theRXTEmission. It concludes by citing some of the scientific capabilities a proposed follow‐on mission will need in order to be successful. © 2004 American Institute of Physics