The phenomenon of surge in an axial flow compressor has long eluded the analytical fluid dynamist. In the recent years, a growing degree of improvement and sophistication in the design of axial flow compressors to achieve higher pressure ratios has resulted in increasingly narrow domains of stable operation. A search for improving stability margins revealed the importance of the blade tip region and casing treatments. The authors have approached the problem by both experimental and analytical methods. The results are mutually confirming. Important new inroads have been made in understanding the flow in the blade tip region, operation of casing treatments and the mechanism of the onset of surge. Some significant conclusions in the selection and design of casing treatments and their effects on the stability margin are presented and explained on the basis of experimental and theoretical results.