  In this work, we examine the propagation of gravitational waves in
cosmological and astrophysical spacetimes in the context of
Einstein--Gauss-Bonnet gravity, in view of the GW170817 event. The perspective
we approach the problem is to obtain a theory which can produce a gravitational
wave speed that is equal to that of light in the vacuum, or at least the speed
can be compatible with the constraints imposed by the GW170817 event. As we
show, in the context of Einstein--Gauss-Bonnet gravity, the propagation speed
of gravity waves in cosmological spacetimes can be compatible with the GW170817
event, and we reconstruct some viable models. However, the propagation of
gravity waves in spherically symmetric spacetimes violates the GW170817
constraints, thus it is impossible for the gravitational wave that propagates
in a spherically symmetric spacetime to have a propagating speed which is equal
to that of light in the vacuum. The same conclusion applies to the
Einstein--Gauss-Bonnet theory with two scalars. We discuss the possible
implications of our results on spherically symmetric spacetimes.
