Classical physics is fine for modeling our everyday life. However, as we learn more we must refine our models. For example, light was once modeled as only a wave. Now it is modeled as a wave and a particle. My grad school is almost 30 years ago so maybe someone else can update. Similarly, gravity is modeled as a wave? particle? other? Go figure. Time for a cool one.
In Einstein's theories, neither. Rather modeled as a distortion of "space-time". However Einstein's theories do not include quantum effects. At the time he wasn't very fond of quantum mechanics, saying "God does not play dice with the universe", later he modified his views. Someone else, Hawking maybe, later responded, "Not only does God play dice with the universe, He sometimes throws them where they can't be seen". :)
More modern treatments attempt to include quantum effects, but a satisfactory general quantum theory of gravitation still does not exist. If it did, one suspects it would settle this "zero point energy" question. But maybe not.