After the current upgrade to their so-called enhanced level, the detectors are evolving toward their second generation: the advanced Virgo and LIGO detectors. LIGO already detected gravitational waves in 2015 and further sensitivity upgrades promise many more detections to follow. But the sensitivity needed to test Einstein's theory of gravity in strong field conditions or to realize a precision gravitational wave astronomy, mainly of massive stellar bodies or of highly asymmetric (in mass) binary stellar systems goes beyond the expected performances of the advanced detectors and of their subsequent upgrades.