  It is well known that Einstein's General Relativity (GR) achieved a great
success and overcame lots of experimental tests. On the other hand, GR also
showed some shortcomings and flaws which today advise theorists to ask if it is
the definitive theory of gravity. In this review we show that, if advanced
projects on the detection of Gravitational Waves (GWs) will improve their
sensitivity, allowing to perform a GWs astronomy, understanding if Einstein's
GR is the correct and definitive theory of gravity will be possible. For this
goal, accurate angular and frequency dependent response functions of
interferometers for GWs arising from various Theories of Gravity, i.e. GR and
Extended Theories of Gravity will have to be used. This review is founded on
the Essay which won an Honorable Mention at the the 2009 Gravity Research
Foundation Awards.
