Supersonic shear layers have inherent low mixing rates due to compressibility effects. Their mixing rate relative to subsonic shear layers can be up to 5 times lower. Several important technological applications which require intense mixing of supersonic flows gave impetus to research aimed to develop methods to enhance mixing in compressible flows with minimal performance penalty. This paper reviews some of these methods applied to both planar shear layers and jets. The methods are arranged in several categories: passive and active control of shear layer instabilities, three dimensional jets, generation of axial vorticity and shock interaction with shear layers. The paper concludes by discussing the importance of the wide range of length-scales in which turbulent mixing occurs.