Three immediate conclusions:

• Light is also curved by the gravitational force, even if according to the Newton's law, the force of gravity acting on light (massless photon) is zero.
• Light, emitted toward the source of gravity, will experience Doppler blueshift; light emitted from the source of gravity will experience Doppler redshift.
• All physical processes should run slower in the presence of gravity.

All these conclusions have been tested experimentally.

Geometry

In the presence of gravity filed, an inertial observer is not necessarily moving in a straight line (orbiting Space Shuttle). Thus, gravity makes straight lines curved, in other words, it changes the geometry of space, or, more precisely (the SR is still valid!), the geometry of space-time.

Thus, the GR is a theory of a curved (i.e. non-flat) space-time.