Work on rotating stall and its related disturbances have been in progress since the Second World War. During this period, certain “hot topics” have come to the fore—mostly in response to pressing problems associated with new engine designs. This paper will take a semihistorical look at some of these fields of study (stall, surge, active control, rotating instabilities, etc.) and will examine the ideas which underpin each topic. Good progress can be reported, but the paper will not be an unrestricted celebration of our successes because, after 75 years of research, we are still unable to predict the stalling behavior of a new compressor or to contribute much to the design of a more stall-resistant machine. Looking forward from where we are today, it is clear that future developments will come from CFD in the form of better performance predictions, better flow modeling, and improved interpretation of experimental results. It is also clear that future experimental work will be most effective when focussed on real compressors with real problems—such as stage matching, large tip clearances, eccentricity, and service life degradation. Today’s topics of interest are mostly associated with compressible effects and so further research will require more high-speed testing.