  Radio interferometry is a powerful technique for astronomical imaging. The
theory of Compressed Sensing (CS) has been applied recently to the ill-posed
inverse problem of recovering images from the measurements taken by radio
interferometric telescopes. We review novel CS radio interferometric imaging
techniques, both at the level of acquisition and reconstruction, and discuss
their superior performance relative to traditional approaches. In order to
remain as close to the theory of CS as possible, these techniques necessarily
consider idealised interferometric configurations. To realise the enhancement
in quality provided by these novel techniques on real radio interferometric
observations, their extension to realistic interferometric configurations is
now of considerable importance. We also chart the future direction of research
required to achieve this goal.
