  General relativity has predicted the existence of gravitational waves (GW),
which are waves of the distortions of space-time with two degrees of
polarization and the propagation speed of light. Alternative theories predict
more polarizations, up to a maximum of six, and possible deviation of
propagation speed from the light speed. The present paper reviews recent
proposals to test the gravity theories in the radiation regime by observing GWs
using pulsar timing arrays.
