The achievements resulting from the application of advanced pulsed power to the generation of high power microwaves (HPM) have included the generation of multi-gigawatt pulses of RF energy. The power achievable is orders of magnitude greater than conventional microwave sources can generate. However, the introduction of the HPM technology into logical applications has been limited to date due to the phenomenon of pulse shortening in which the RF pulse terminates before the pulse power source used to produce it. Conventional microwave tubes can generate a few to 10 MW of power with pulsewidths of many microseconds when required. High power microwave sources can produce gigawatts of power, but only for relatively short pulsewidths, typically tens to hundreds of nanoseconds. An international effort during the past few years has generated important new discoveries toward the elimination of pulse shortening. Some of the new techniques have the potential for helping the conventional tube industry as well as being practical for high power microwave sources. This paper reviews the pulse shortening problem, its causes, and the worldwide scope and direction of research conducted to date to resolve it. The paper also discusses the potential remedies for the problem and recommends a course of research to further progress on the issue.