Spike-stall is a fast stall mode of both axial and centrifugal compressors.It can very quickly lead to surge and interrupt the normal operation of compressors.Despite decades efforts,we still do not have a clear picture of how it starts and develops,let alone predicting it.This paper reviews the research works on this instability of compressors,describes the progress made,discusses the shortcomings of current research,and proposes some new concepts that may lead to breakthroughs.It is pointed out that current methods of predicting spike-stall are mostly based on classic stability concept which is incapable of handling the transient growth and diminution of disturbances in short length scales that typify spike-stall.Modern transient instability concept is proposed that establishes the link between the maximum amplification of the system to initial perturbations and time.The non-normality of compressor system is also emphasised.